A Sasaki-like almost contact complex Riemannian manifold is defined as an almost contact complex Riemannian manifold which complex cone is a holomorphic complex Riemannian manifold. Explicit compact and non-compact examples are given. A canonical construction producing a Sasaki-like almost contact complex Riemannian ma…
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48 results for “complex manifolds”
Study Hilbert complexes on complex manifolds.
problem Analyse Hilbert complexes on complex manifolds.
method Define and study Aeppli-Bott-Chern Hilbert complex; examine properties on various manifolds; use self-adjoint extensions of differential operators.
result Kernels of operators on compact Hermitian manifolds are isomorphic to Aeppli or Bott-Chern cohomology.
Study Hodge-de Rham numbers for almost complex 4-manifolds, extending properties from complex surfaces.
problem Understanding Hodge-de Rham numbers for almost complex 4-manifolds.
method Introduced and studied Hodge-de Rham numbers, extending properties from complex surfaces.
result All Hodge-de Rham numbers for compact almost complex 4-manifolds are determined by the cohomology, except for one (the irregularity).
Study on GL(2) geometries on complex manifolds, focusing on Kähler-Einstein and Fano manifolds.
problem Characterizing compact complex manifolds with holomorphic GL(2)-geometry.
method Analyzing Kähler-Einstein and Fano manifolds, using GL(2) and SL(2) geometries.
result Only compact Kähler-Einstein manifolds with holomorphic GL(2)-geometry are covered by compact complex tori, three dimensional quadric, or three dimensional Lie ball.
Newlander-Nirenberg theorem extended to complex b-manifolds.
problem Characterizing complex b-manifolds.
method Involutive splitting of b-tangent bundle, formal local invariants, singular coordinate change.
result Complex b-manifolds have a single local model.
Study on complex line fields on almost-complex manifolds, proving existence conditions.
problem Existence of linearly independent complex line fields on almost-complex manifolds.
method Prove necessary and sufficient conditions for the existence of one, two, or three fields over certain manifolds.
result Necessary and sufficient condition for the existence of complex line fields over certain manifolds.
Study on complex submanifolds in Endo-Pajitnov manifolds.
problem Existence and characterization of complex submanifolds in Endo-Pajitnov manifolds.
method Identification of a class of Endo-Pajitnov manifolds containing compact complex submanifolds and establishment of an algebraic condition for the absence of compact complex curves.
result Established an algebraic condition for the absence of compact complex curves in Endo-Pajitnov manifolds.
We classify all closed non-orientable P2-irreducible 3-manifolds having complexity up to 6 and we describe some having complexity 7. We show in particular that there is no such manifold with complexity less than 6, and that those having complexity 6 are precisely the 4 flat non-orientable ones and the filling of the Gi…
New proof shows 4-manifolds can't support complex structures.
problem Proving 4-manifolds can't support complex structures.
method New proof of complex structure non-existence for real-hyperbolic 4-manifolds.
result Extended graph 4-manifolds with positive Euler characteristic cannot support a complex structure.
Condition for intersection of real flag manifolds in complex flag manifold.
problem Intersection conditions of real flag manifolds in a complex flag manifold.
method Condition given in terms of symmetric triad, antipodal intersection proven.
result Intersection of real flag manifolds is antipodal.
The paper introduces surface-complexity to measure 3-manifold complexity.
problem Measuring the complexity of compact 3-manifolds.
method Defining surface-complexity via Dehn surfaces and proving its properties.
result Surface-complexity equals the minimal number of cubes in a cubulation for certain manifolds.
New class of singular complex manifolds studied with degenerate theory.
problem Understanding singular complex manifolds.
method Developed degenerate Kodaira-Hodge theory for new class.
result New degenerate theory for singular complex manifolds.
Research confirms a conjecture about complex manifolds with total Betti number three.
problem Understanding the minimal total Betti number of closed almost complex manifolds.
method Analyzing properties of almost complex manifolds and using topological results.
result The only simply connected closed complex manifold with total Betti number three is the complex projective plane.
Paper generalizes ddc-condition to non-Kähler complex manifolds.
problem Characterizing complex manifolds beyond Kähler geometry.
method Introduces and studies a new ddc-type condition for complex manifolds.
result The new condition is open under deformations and applies to various manifolds.
The paper describes complex structures on Oeljeklaus-Toma manifolds.
problem Investigating different complex structures on Oeljeklaus-Toma manifolds.
method Algebraic description of biholomorphic manifolds obtained by conjugating complex embeddings.
result Compact non-Kähler manifolds with multiple rigid complex structures.
Compactify complex hyperbolic almost Hermitian manifolds.
problem Understanding the geometric structure of complex hyperbolic almost Hermitian manifolds.
method Analyzing the asymptotic curvature and boundary conditions of the manifold.
result The interior of a compact almost complex manifold can represent the original manifold.
We classify all closed non-orientable P2-irreducible 3-manifolds with complexity up to 7, fixing two mistakes in our previous complexity-up-to-6 classification. We show that there is no such manifold with complexity less than 6, five with complexity 6 (the four flat ones and the filling of the Gieseking manifold, which…
Kähler complexity one Hamiltonian T-manifolds have trivial paintings.
problem Understanding the structure of Kähler complexity one Hamiltonian T-manifolds.
method Proving the existence of a trivial painting for compact, connected Kähler complexity one Hamiltonian T-manifolds.
result Every compact, connected Kähler complexity one Hamiltonian T-manifold has a trivial painting.
The paper defines and constructs almost complex blow-ups on 4D almost complex manifolds.
problem Existence and uniqueness of almost complex blow-ups on almost complex manifolds.
method Definition and construction of almost complex blow-ups, proving their existence and uniqueness.
result Existence and uniqueness of almost complex blow-ups on 4D almost complex manifolds.
Classifies Nil 3-manifolds as cross-sections of complex hyperbolic surfaces.
problem Identifying Nil 3-manifolds as cross-sections of complex hyperbolic surfaces.
method Comprehensive classification of commensurability classes of cusped, arithmetic, and non-arithmetic complex hyperbolic 2-manifolds.
result Some Nil 3-manifolds are cross-sections in every commensurability class, while others are cross-sections in only one.
Study proposes a functional for LCK metrics on complex manifolds.
problem Existence problem for locally conformally Kähler metrics on compact complex manifolds.
method Introducing and studying a functional that varies by complex dimension.
result Functional approach to existence problem for LCK metrics.
Study on harmonicity of complex structure on product of trans-Sasakian manifolds.
problem Investigating harmonicity of complex structure on product of trans-Sasakian manifolds.
method Analysis of Levi-Civita connection and conditions for harmonicity on product manifold.
result Conditions for harmonicity of complex structure on product manifold of trans-Sasakian manifolds.
Generalizes complex manifolds to manifolds with corners and generalized corners.
problem Tackles the extension of complex structures to manifolds with corners and generalized corners.
method Uses complex structures on the b-tangent bundle and proves a formal Newlander-Nirenberg type theorem.
result Proves that along each corner stratum, the b-complex structure agrees with a standard model to infinite order.
A Theorem of Wang in [Wa] implies that any holomorphic parallelism on a compact complex manifold M is flat with respect to some complex Lie algebra structure whose dimension coincides with that of M. We study here rational parallelisms on complex manifolds. We exhibit rational parallelisms on compact complex manifolds …
Small Nijenhuis tensor found on compact manifolds.
problem Finding compact manifolds with small Nijenhuis tensor.
method Provided explicit examples of manifolds with small Nijenhuis tensor.
result Examples of manifolds with small Nijenhuis tensor in various dimensions.
Proposed theorems for lifts of the extended almost complex structures on the complex manifoldmath.DG
The paper studies lifts of complex structures on a manifold.
problem Understanding higher-order lifts of extended almost complex structures.
method Proved theorems on Nijenhuis tensor and introduced a new tensor field.
result Basic results on almost analytic complex vectors are investigated.
New class of complex manifolds defined, properties studied.
problem Understanding properties of complex manifolds.
method Introduced and studied wHHR manifolds, proved metric equivalence.
result Bergman and Kobayashi metrics are biLipschitz equivalent for wHHR Stein manifolds.
Researchers found the minimum number of tetrahedra needed to triangulate elliptic and sol 3-manifolds.
problem Finding the minimum number of tetrahedra in triangulations of 3-manifolds.
method Computed the triangulation complexity of all elliptic and sol 3-manifolds, within a bounded error.
result Computed the triangulation complexity of all elliptic and sol 3-manifolds.
Complex structures found on product of Sasakian manifolds.
problem Exploring complex structures on the product of two Sasakian manifolds.
method Examined a family of complex structures on the product of two compact Sasakian manifolds, computed Dolbeault cohomology groups.
result None of the complex structures in the family admit compatible locally conformally Kähler metrics if both Sasakian manifolds are of dimension greater than 1.
Penrose's two-spinor notation for -dimensional Lorentzian manifolds can be extended to two-component notation for quaternionic manifolds, which is a very useful tool for calculation. We construct a family of quaternionic complexes over unimodular quaternionic manifolds by elementary calculation. On complex quaternio…
The paper explores -Kähler structures on complex manifolds and their properties.
problem Addressing conjectures on specific types of complex manifolds and their structures.
method Analyzing -Kähler nilmanifolds and holomorphically parallelizable nilmanifolds, deriving necessary conditions for smooth curves of -Kähler structures, studying cohomology classes, and providing examples.
result Derives necessary conditions for the existence of smooth curves of -Kähler structures and provides examples of compact complex manifolds with -Kähler structures.
Complexity of PL-manifoldsmath.GT
We extend Matveev's complexity of 3-manifolds to PL compact manifolds of arbitrary dimension, and we study its properties. The complexity of a manifold is the minimum number of vertices in a simple spine. We study how this quantity changes under the most common topological operations (handle additions, finite coverings…
Following T.-J. Li, W. Zhang [Comparing tamed and compatible symplectic cones and cohomological properties of almost complex manifolds, Comm. Anal. Geom.], we continue to study the link between the cohomology of an almost-complex manifold and its almost-complex structure. In particular, we apply the same argument in [T…
The paper finds manifold structures on complex spaces.
problem Constructing manifold structures on highly connected Poincaré complexes.
method Constructing examples and determining homotopy types.
result Examples of highly connected Poincaré complexes are found to be homotopy equivalent to manifolds but not smooth.
Study cohomology of Bigolin complex on complex manifolds.
problem Characterize cohomology of Bigolin complex on compact complex manifolds.
method Analyze the decomposition of the double complex into squares and zigzags, focusing on the zigzags contributing to cohomology.
result In complex dimension 3, multiplicities of zigzags are characterized by Betti, Hodge, Aeppli numbers plus Bigolin numbers.
We define and study branched shadows of 4-manifolds as a combination of branched spines of 3-manifolds and Turaev's shadows. We use these objects to combinatorially represent 4-manifolds equipped with -structures and homotopy classes of almost complex structures. We then use branched shadows to study complex 4-…
In this work we study the existence of invariant almost complex structures on real flag manifolds associated to split real forms of complex simple Lie algebras. We show that, contrary to the complex case where the invariant almost complex structures are well known, some real flag manifolds do not admit such structures.…
It is known since 1954 that every 3-manifold bounds a 4-manifold. Thus, for instance, every 3-manifold has a surgery diagram. There are several proofs of this fact, including constructive proofs, but there has been little attention to the complexity of the 4-manifold produced. Given a 3-manifold M of complexity n, we s…
Iwasawa manifold is a compact complex homogeneous manifold isomorphic to a quotient of the group of complex unipotent matrices by a cocompact lattice. We prove that any compact complex curve in an Iwasawa manifold is contained in a holomorphic torus. We also prove that any Kähler surface in an Iwasawa mani…
The paper extends Montel's theorem to complex Finsler manifolds.
problem Understanding normal families of holomorphic mappings in complex Finsler geometry.
method Proves a theorem for normal families of holomorphic mappings between complex Finsler manifolds.
result Extends Montel's theorem to complex Finsler manifolds.
The paper explores complex Poisson structures on smooth functions in complex manifolds.
problem Exploring complex Poisson structures on smooth functions in complex manifolds.
method Considering structures of complex Poisson brackets generated by a -form.
result Examples of complex Poisson structures are provided in $\C^\ast$.
We establish plurisubharmonicity of the envelope of Poisson and Lelong functionals on almost complex manifolds. That is, we generalize the corresponding results for complex manifolds and almost complex manifolds of complex dimension two. We also provide some applications to the regularization of J-plurisubharmonic func…
Study on automorphisms of complex -manifolds, extending previous work.
problem Investigate automorphisms of complex -manifolds with higher-order degeneracies.
method Extend Mendoza's definition of complex -manifolds to complex -manifolds and study their local and global automorphisms.
result Propose -analogues for classical spaces of holomorphic functions.
We describe an algorithm which has enabled us to give a complete list, without repetitions, of all closed oriented irreducible 3-manifolds of complexity up to 9. More interestingly, we have actually been able to give a "name" to each such manifold, by recognizing its canonical decomposition into Seifert fibred spaces a…
We define an invariant, which we call surface-complexity, of closed 3-manifolds by means of Dehn surfaces. The surface-complexity of a manifold is a natural number measuring how much the manifold is complicated. We prove that it fulfils interesting properties: it is subadditive under connected sum and finite-to-one on …
The paper explores Kodaira dimension on almost complex manifolds.
problem Understanding Kodaira dimension on non-integrable almost complex manifolds.
method Generalization of Kodaira dimension to almost complex manifolds and study of its behavior under deformations.
result Kodaira dimension is invariant under holomorphic deformations for smooth projective manifolds but not for non-projective manifolds.
The graph complexity of a compact 3-manifold is defined as the minimum order among all 4-colored graphs representing it. Exact calculations of graph complexity have been already performed, through tabulations, for closed orientable manifolds (up to graph complexity 32) and for compact orientable 3-manifolds with toric …
Paper constructs subcomplexes from filtered Riemannian manifolds.
problem Understanding subcomplexes on filtered Riemannian manifolds.
method General construction of subcomplexes from two distinct complexes.
result Aligns with Rumin complex on regular subRiemannian manifolds.