Almost para-Hermitian manifold it is manifold equipped with almost para-complex structure and compatible pseudo-metric of neutral signature. It is considered a class of immersions of almost para-Hermitian manifolds into almost para-Hermitian manifolds. Such immersions are called slant submanifolds. The concept is an an…
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48 results for “almost Hermitian manifolds”
Holomorphic maps are a special case of Hermitian pluriharmonic maps between almost Hermitian manifolds.
problem Characterizing maps between almost Hermitian manifolds.
method Introducing Hermitian pluriharmonic maps and proving their properties.
result Holomorphic or anti-holomorphic maps are Hermitian pluriharmonic.
The paper proves Liouville theorems for holomorphic maps on pseudo-Hermitian manifolds.
problem Proving Liouville theorems for holomorphic maps on pseudo-Hermitian manifolds.
method Analyzing maps between different classes of pseudo-Hermitian manifolds, using curvature assumptions.
result Holomorphic maps are constant under certain curvature conditions.
In this paper, by using the Bochner technique on almost Hermitian manifolds, we obtain a complex Hessian comparison for almost Hermitian manifolds generalizing the Laplacian comparison for almost Hermitian manifolds by Tossati, and reprove a diameter estimate for almost Hermitian manifolds by Gray. Moreover, we obtain …
Characterizes a class of almost Hermitian 4-manifolds using integral identities.
problem Global characterization of almost Hermitian 4-manifolds.
method Using an integral identity from Sekigawa's work, proving a uniqueness result on Lie algebras.
result Global characterization of the class of almost Hermitian 4-manifolds.
Paper generalizes sub-slope definition and solves complex equations on compact manifolds.
problem Solving complex equations on compact almost Hermitian manifolds.
method Generalized sub-slope definition and proved existence of solutions for a class of equations.
result Solved complex Hessian quotient and deformed Hermitian-Yang-Mills equations.
Paper proves solutions for deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds.
problem Existence of solutions for deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds.
method Derive a priori estimates under the existence of an admissible -subsolution; prove existence of solutions under the condition of existence of a supersolution.
result Proves existence of solutions for the deformed Hermitian-Yang-Mills equation.
Study various submanifolds in quaternionic skew-Hermitian spaces.
problem Characterize submanifolds in almost quaternionic skew-Hermitian manifolds.
method Construct explicit examples of submanifolds in semisimple quaternionic skew-Hermitian symmetric spaces.
result Explicit examples of submanifolds for each type considered.
The covariant derivative of the Kähler form of an almost pseudo-Hermitian or of an almost para-Hermitian manifold satisfies certain algebraic relations. We show, conversely, that any 3-tensor which satisfies these algebraic relations can be realized geometrically.
In this paper, by introducing a notion of local quasi holomorphic frame, we obtain a curvature formula for almost Hermitian manifolds which is similar to that of Hermitian manifolds. Moreover, as applications of the curvature formula, we extend a result of H.S. Wu and a result of F. Zheng to almost Hermitian manifolds.
The paper studies equations on almost Hermitian manifolds with estimates and existence results.
problem Solving Monge-Ampère type equations on compact almost Hermitian manifolds.
method Derives a priori estimates and obtains existence results under admissible conditions.
result Existence of solutions under admissible conditions for Monge-Ampère type equations.
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.
Paper establishes estimates for solutions on compact manifolds.
problem Solving fully non-linear equations on compact almost Hermitian manifolds.
method Establishes a priori estimates for solutions.
result Solves complex Hessian and Monge-Ampère equations.
The Schur's theorem of antiholomorphic type is proved for arbitrary almost Hermitian manifolds, namely: If a connected almost Hermitian manifold of dimension greater or equal to 6 is of pointwise constant antiholomorphic sectional curvature, then this curvature is a global constant.
The paper explores Kähler-like metrics on generalized flag manifolds.
problem Finding invariant almost Hermitian structures with specific scalar curvature properties.
method Investigating invariant almost Hermitian geometry on generalized flag manifolds, focusing on Kähler-like metrics.
result Examples of Kähler-like metrics satisfying are provided.
Study shows that dimension of Dolbeault harmonic forms is not always equal to B- on certain 4-manifolds.
problem Determining the dimension of Dolbeault harmonic (1,1)-forms on almost Hermitian 4-manifolds.
method Provided examples and proved non-equality of and for certain structures.
result Dimension of Dolbeault harmonic (1,1)-forms is not always equal to B- on almost Hermitian 4-manifolds.
New operators generalize Michelsohn's on almost Hermitian manifolds.
problem Generalizing differential operators to almost Hermitian manifolds.
method Introducing two differential operators on sections of the complex Clifford bundle over compact almost Hermitian manifolds.
result Surprising Kähler-like symmetries in the kernel of the Laplacians of these operators.
The paper studies quarter-symmetric connections on Hermitian and Kähler manifolds.
problem Examining quarter-symmetric connections on almost Hermitian and Kähler manifolds.
method Analyzing the curvature tensors and their properties with respect to quarter-symmetric connections.
result Constructed tensors that do not depend on the quarter-symmetric connection generator, including the Weyl projective curvature tensor.
The paper explores curvature constraints on Kodaira dimension for specific almost Hermitian manifolds.
problem Investigating Riemannian curvature constraints on the Kodaira dimension of compact almost Hermitian manifolds.
method Analyzing compact almost Hermitian manifolds in the Gray-Hervella class and Hermitian manifolds with nonnegative scalar curvature.
result For compact almost Hermitian manifolds with nonnegative scalar curvature, the Kodaira dimension is either -∞ or 0, with specific conditions.
Almost Hermitian Ricci flowmath.DG
We introduce a new curvature flow which matches with the Ricci flow on metrics and preserves the almost Hermitian condition. This enables us to use Ricci flow to study almost Hermitian manifolds.
The study proves conditions for Hermitian metrics on compact almost complex manifolds.
problem Conditions for Hermitian metrics on compact almost complex manifolds.
method Analyzes compact almost complex manifolds with Hermitian metrics and integral conditions involving -harmonic -forms.
result The integral condition is automatically satisfied for strongly Gauduchon metrics, and equivalent to being strongly Gauduchon for integrable almost complex structures.
We give a condition for an almost constant-type manifold to be a constant-type manifold, and holomorphic and -invariant submanifolds of almost Hermitian manifolds are studied. Generalizations of some results in [5] are given.
Study of almost Yamabe solitons on Kaehler submersions.
problem Characterizing almost Yamabe solitons on Kaehler submersions.
method Analyzing conditions for solitons to be shrinking, steady, or expanding.
result Characterizations for almost Yamabe solitons in terms of extrinsic horizontal scalar curvature.
New algebraic structures for Hermitian geometry cohomologies.
problem Understanding cohomologies of Hermitian manifolds.
method Introducing BV-algebras and homotopy BV-algebras.
result Cohomologies of Hermitian manifolds are endowed with homotopy hypercommutative algebra structures.
Study computes invariants on six-dimensional solvmanifolds, providing symplectic structure obstructions.
problem Computing invariants on six-dimensional solvmanifolds.
method Computed almost-complex and almost-Hermitian invariants on families of solvmanifolds.
result Provides obstructions to symplectic structures on compact almost-complex manifolds.
Paper solves complex Monge-Ampère equation on almost Hermitian manifolds.
problem Solving Dirichlet problem for complex Monge-Ampère equation.
method Properties of subsolutions for fully nonlinear elliptic equations.
result Existence of -smooth strictly -plurisubharmonic subsolution.
Extends three circle theorem to almost Hermitian manifolds.
problem Three circle theorem for Kähler manifolds to almost Hermitian manifolds.
method General maximum principle established to prove three circle theorem.
result Sharp dimension estimates and Liouville theorems for holomorphic functions.
The canonical connection on a Riemannian almost product manifold is an analogue to the Hermitian connection on an almost Hermitian manifold. In this paper we consider the canonical connection on a class of Riemannian almost product manifolds with non-integrable almost product structure. We construct and characterize an…
Tubular neighborhoods play an important role in differential topology. We have applied these constructions to geometry of almost Hermitian manifolds. At first, we consider deformations of tensor structures on a normal tubular neighborhood of a submanifold in a Riemannian manifold.Further, an almost hyperHermitian struc…
The paper classifies flag manifolds with specific isotropy components and finds conditions for Kähler-like scalar curvature.
problem Classifying flag manifolds with specific isotropy components and finding conditions for Kähler-like scalar curvature.
method Investigating invariant almost Hermitian structures on generalized flag manifolds with two or three irreducible components.
result Classification of flag manifolds admitting Kähler-like scalar curvature and conditions for such structures.
Almost hypercomplex manifolds with Hermitian and anti-Hermitian metrics are considered. A linear connection is introduced such that the structure of these manifolds is parallel with respect to D. Of special interest is the class of the locally conformally equivalent manifolds of the manifolds with covariantly const…
Paper solves a metric-independent problem on almost Kähler 4-manifolds.
problem Find a metric-independent generalization of Bott-Chern and Aeppli numbers.
method Introduced a new approach to generalize Bott-Chern and Aeppli numbers.
result Found a solution valid on almost Kähler 4-manifolds.
The Almost Hermitian Curvature flow was introduced by Streets and Tian in order to study almost hermitian structures, with a particular interest in symplectic structures. This flow is given by a diffusion-reaction equation. Hence it is natural to ask the following: which almost hermitian structures are dynamically stab…
In this paper, we systematically compute the Bianchi identities for the canonical connection on an almost Hermitian manifold. Moreover, we also compute the curvature tensor of the Levi-Civita connection on almost Hermitian manifolds in terms of curvature and torsion of the canonical connection. As applications of the c…
We obtain conditions on the Lee form under which a holomorphic map between almost Hermitian manifolds is a harmonic map or morphism. Then we discuss under what conditions (i) the image of a holomorphic map from a cosymplectic manifold is also cosymplectic, (ii) a holomophic map with Hermitian image defines a Hermitian …
Almost Hermitian Identitiesmath.DG
Study local commutation relation on almost complex manifolds.
problem Local commutation relation between Lefschetz operator and exterior differential.
method Analyzing almost complex manifolds with compatible metrics.
result Generalizes local Kähler identities to almost Hermitian manifolds.
Criterions for constancy of the holomorphic sectional curvature and the antiholomorphic sectional curvature are proved for almost Hermitian manifolds. It is shown, that an almost Hermitian manifold satisfying the axiom of antiholomorphic planes or the axiom of antiholomorphic spheres is a real or a complex space form.
We prove the following results: An almost Hermitian manifold of indefinite metric is of pointwise constant holomorphic sectional curvature if the holomorphic sectional curvature is bounded from above and from below. If the antiholomorphic sectional curvature is bounded either from above or from below, then the manifold…
It is introduced a differentiable manifold with almost contact 3-structure which consists of an almost contact metric structure and two almost contact B-metric structures. The product of this manifold and a real line is an almost hypercomplex manifold with Hermitian-Norden metrics. It is proven that the introduced mani…
Construct a Hermitian metric on non-Hermitian Yang--Mills moduli spaces near the Hermitian locus.
problem Moduli space of non-Hermitian Yang--Mills connections over a compact Kähler manifold
method Using normalized harmonic metrics
result Near the Hermitian locus, the unobstructed locus carries an almost hypercomplex structure compatible with the associated Riemannian metric.
We prove a version of Yau's Schwarz Lemma for general almost-complex manifolds equipped with Hermitian metrics. This requires an extension to this setting of the Laplacian comparison theorem. As an application we show that the product of two almost-complex manifolds does not admit any complete Hermitian metric with bis…
The paper explores constant holomorphic d-scalar curvature on specific manifolds.
problem Existence and prescription of constant holomorphic d-scalar curvature.
method Study of closed, connected almost Hermitian manifolds of dimension .
result Obtained an application and variation formula for a conformal invariant.
The paper extends Bott-Chern Laplacian definition and explores its properties on almost Hermitian manifolds.
problem Exploring the properties of Bott-Chern Laplacian on almost Hermitian manifolds.
method Extending the definition of Bott-Chern Laplacian, proving ellipticity, and analyzing kernels on different types of manifolds.
result The dimensions of Bott-Chern and Dolbeault harmonic forms differ on almost complex 4-manifolds with specific metrics.
The object of investigations are almost hypercomplex structures with Hermitian-Norden metrics on 4-dimensional Lie groups considered as smooth manifolds. There are studied both the basic classes of a classification of 4-dimensional indecomposable real Lie algebras depending on two parameters. Some geometric characteris…
We compute the structure groups of almost even-Clifford Hermitian manifolds and determine when such groups lead to Spin structures.
Study on 4D Lie groups and related almost hypercomplex manifolds.
problem Characterizing almost hypercomplex manifolds with specific metrics.
method Construction and classification of manifolds based on Lie algebras.
result Established a connection between Lie algebra classes and manifold classifications.
A Theorem of Kirichenko states that the torsion 3-form of the characteristic connection of a nearly Kähler manifold is parallel. On the other side, any almost hermitian manifold of type admits a unique connection with totally skew symmetric torsion. In dimension six, we generalize Kirichenko's Theorem an…
The subject of investigations are the almost hypercomplex manifolds with Hermitian and anti-Hermitian (Norden) metrics. A linear connection D is introduced such that the structure of these manifolds is parallel with respect to D and its torsion is totally skew-symmetric. The class of the nearly Kaehler manifolds with r…