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 contact manifolds”
Study on null hypersurfaces in complex contact manifolds.
problem Characterizing null hypersurfaces in indefinite complex contact manifolds.
method Proved classification results for various null hypersurfaces and characterized the ambient space.
result The ambient complex contact manifold must have constant -sectional curvature of for certain null hypersurfaces.
The paper connects complex contact structures to specific types of almost contact 3-structures.
problem Understanding the relationship between complex contact structures and almost contact 3-structures.
method Proving that every complex contact structure gives rise to a distinguished almost contact metric 3-structure.
result The paper provides new examples of manifolds with specific contact and almost contact structures.
Complex contact manifolds, varieties of minimal rational tangents, and exterior differential systemsmath.AG
The abstract discusses classification theorems for complex contact manifolds and their geometric properties.
problem Classifying complex contact manifolds and understanding their geometric properties.
method Analyzing contact lines and varieties of minimal rational tangents.
result Partial classification theorems for projective complex contact manifolds.
Study of local structure of generalized contact bundles.
problem Little is known about the local structure of generalized contact bundles.
method Proved a local splitting theorem similar to those in Poisson geometry.
result In a neighborhood of a regular point, a generalized contact bundle is either the product of a contact and a complex manifold or the product of a symplectic manifold and a manifold with an integrable complex structure.
The study defines and analyzes semi-invariant submanifolds in complex contact metric manifolds.
problem Characterizing semi-invariant submanifolds in complex contact metric manifolds.
method Definition and derivation of relations, integrability conditions of distributions.
result Obtained useful relations and integrability conditions for semi-invariant submanifolds.
In this paper, we study normal complex contact metric manifolds and we get some general results on them. Moreover, we obtained the general expression of the curvature tensor field for arbitrary vector fields. Furthermore, we show that the necessary and succient conditions to be normal a complex contact metric manifold.…
Paper proves stability of pseudo-Einstein contact form existence.
problem Stability of pseudo-Einstein contact form existence under deformations.
method Deformations of real hypersurfaces in complex manifolds.
result Existence of pseudo-Einstein contact form is preserved under deformations.
We prove rigidity and vanishing theorems for several holomorphic Euler characteristics on complex contact manifolds admitting holomorphic circle actions preserving the contact structure. Such vanishings are reminiscent of those of LeBrun and Salamon on Fano contact manifolds but under a symmetry assumption instead of a…
A connected Fano complex-contact manifold is isomorphic to the kaehlerian C-space of Boothby type with a natural complex-contact structure corresponding to a non-abelian simple complex Lie algebra if the contact line bundle is very ample. A. Beauville relaxed the provision to two assumptions that the contact line bundl…
On normal contact pairsmath.DG
We consider manifolds endowed with a contact pair structure. To such a structure are naturally associated two almost complex structures. If they are both integrable, we call the structure a normal contact pair. We generalize the Morimoto's Theorem on product of almost contact manifolds to flat bundles. We construct som…
Holomorphic Jacobi manifolds integrate to complex contact groupoids.
problem Integrating holomorphic Jacobi manifolds.
method Homogenization scheme to identify and integrate holomorphic Jacobi manifolds to complex contact groupoids.
result Holomorphic Jacobi manifolds integrate to complex contact groupoids.
The study defines and explores properties of complex Sasakian manifolds.
problem Understanding the geometric structure of complex Sasakian manifolds.
method Definition and analysis of properties, curvature relations, and flatness conditions.
result Obtained useful curvature relations and examined flatness conditions for general curvature tensor B.
Study of contact-complex Riemannian submersions in various manifold classes.
problem Characterizing submersions in specific manifold classes.
method Analyzing properties of O'Neill invariants and discussing integrability and minimality.
result Main properties of O'Neill invariants and integrability/minimality of fibres discussed.
We generalise the notion of contact manifold by allowing the contact distribution to have codimension two. There are special features in dimension six. In particular, we show that the complex structure on a three-dimensional complex contact manifold is determined solely by the underlying contact distribution.
In this paper, we construct complex metric structures on complex hypersurfaces in hyperkahler manifolds. This construction is that in contact geometry.
Study on null submanifolds in indefinite complex contact geometry.
problem Geometry of null submanifolds in indefinite complex contact manifolds.
method Analysis of quaternion null submanifolds and distributions on screen submanifolds.
result Quaternion null submanifolds are always totally geodesic.
Study on Yamabe solitons on specific complex manifolds, focusing on torse-forming vector fields.
problem Exploring Yamabe solitons on a specific class of complex manifolds.
method Analyzing Yamabe solitons on almost contact complex Riemannian manifolds with a vertical torse-forming vector field.
result Explicit examples of 5-dimensional Lie groups characterized by the study.
Sobolev mappings preserve the Rumin complex on contact manifolds.
problem Preserving the Rumin complex under Sobolev mappings on contact manifolds.
method Using the Pullback Theorem, Pansu pullback is shown to induce chain mappings between Rumin complexes and de Rham complexes.
result The Rumin flat complex is bilipschitz invariant under Sobolev mappings between contact manifolds.
Regular Jacobi structures on line bundles lead to generalized contact bundles.
problem Understanding the relationship between Jacobi structures and generalized contact bundles.
method Investigating weakly regular Jacobi structures and their transverse complex structures.
result Conditions for a pair of a regular Jacobi structure and a transverse complex structure to form a generalized contact structure.
The paper proves a splitting theorem for sheaves of holomorphic k-vectors on complex contact manifolds.
problem Understanding the structure of sheaves of holomorphic k-vectors on complex contact manifolds.
method Proving a splitting theorem using sheaves and cohomology.
result The sheaf of holomorphic k-vectors splits into two components.
Weak quasi contact metric manifolds and new characteristics of K-contact and Sasakian manifoldsmath.DG
Study weak quasi contact metric manifolds to generalize K-contact and Sasakian manifolds criteria.
problem Generalize K-contact and Sasakian manifolds criteria using weak quasi contact metric manifolds.
method Study weak quasi contact metric manifolds and generalize theorems for K-contact and Sasakian manifolds.
result Provide new criterions for K-contact and Sasakian manifolds in terms of curvature tensor and geometric objects.
We construct some families of complex structures on compact manifolds by means of normal almost contact structures (nacs) so that each complex manifold in the family has a non-singular holomorphic flow. These families include as particular cases the Hopf and Calabi-Eckmann manifolds and the complex structures on the pr…
Contact Riemannian manifolds, whose complex structures are not necessarily integrable, are generalization of pseudohermitian manifolds in CR geometry. The Tanaka-Webster-Tanno connection plays the role of the Tanaka-Webster connection of a pseudohermitian manifold. Conformal transformations and the Yamabe problem are a…
The paper connects complex spacetimes to twistor spaces and finds an almost contact structure.
problem Understanding the geometry of complex spacetimes and their relation to twistor spaces.
method Using a correspondence between 5D complex spacetimes and 4D twistor spaces, the paper constructs almost contact structures.
result A 5-dimensional K-contact manifold can be derived from the Ren-Wang twistor space.
Paper finds previous work on submanifolds incorrect.
problem Incorrect definition of semi-invariant submanifolds.
method Examined previous work's definition and found it flawed.
result Previous results on semi-invariant submanifolds are invalid.
Holomorphic handle attaching proves complex surface properties.
problem Characterizing complex surfaces with contact boundaries.
method Holomorphic handle attaching method.
result Closed contact 3-manifolds can be filled as complex surfaces' boundaries.
Study on solitons in complex Riemannian manifolds with specific properties.
problem Investigating solitons on specific types of complex Riemannian manifolds.
method Introduced and analyzed almost Riemann solitons on almost contact complex Riemannian manifolds with a vertical potential.
result Derived curvature properties and constructed an explicit example of dimension five.
We consider a pair of smooth manifolds, which are the counterparts in the even-dimensional and odd-dimensional cases. They are separately an almost complex manifold with Norden metric and an almost contact manifolds with B-metric, respectively. They can be combined as the so-called almost contact complex Riemannian man…
A contact hypersurface in a Kaehler manifold is a real hypersurface for which the induced almost contact metric structure determines a contact structure. We carry out a systematic study of contact hypersurfaces in Kaehler manifolds. We then apply these general results to obtain classifications of contact hypersurfaces …
Introduces new holomorphic contact structures and proves unobstructedness theorems.
problem Generalizing classical holomorphic contact and symplectic structures.
method Introducing new classes of holomorphic -contact and -symplectic manifolds, observing their properties, and proving structure and unobstructedness theorems.
result Generalizes classical results on small deformations of complex structures.
Constructive method for contact structures on homogeneous manifolds.
problem Describing contact structures on compact homogeneous contact manifolds.
method Using representation theory of Lie algebras to compute contact forms and Sasaki-Einstein structures.
result Explicit examples of crepant resolutions of Calabi-Yau cones.
Defines generalized Sasakian structures in contact geometry.
problem Understanding k-contact manifolds and CR manifolds.
method Introduced generalized Sasakian structures and proved their equivalence to Sasakian structures.
result k-contact manifolds are generalized Sasakian if and only if they are classically Sasakian.
We collect our recent results ([5] and [8]) and we get the equivalence of the three notions of the title under some conditions. We then use this equivalence in order to prove some consequences about Sasakian manifolds, complex almost contact structures and complex k-contact structures.
Survey of recent results in weak almost contact structures.
problem New geometric structures replacing complex structure in contact manifolds.
method Survey of recent findings in weak almost contact manifolds.
result Recent results on geodesic and Killing fields, rigidity and splitting theorems, etc.
Study of Yamabe solitons on specific geometric manifolds.
problem Characterizing Yamabe solitons on almost contact complex Riemannian manifolds.
method Investigation of two cases: Sasaki-like and torse-forming potentials.
result Explicit examples and theoretical properties confirmed in 3D.
Let Z be a compact complex (2n+1)-manifold which carries a {\em complex contact structure}, meaning a codimension-1 holomorphic sub-bundle D of TZ which is maximally non-integrable. If Z admits a Kähler-Einstein metric of positive scalar curvature, we show that it is the Salamon twistor space of a quaternion-Kähler man…
The paper proves a decomposition theorem for forms on sub-Riemannian contact manifolds.
problem Developing a -Hodge decomposition on sub-Riemannian contact manifolds.
method Using a Sobolev approach and recent results from [4] and [6].
result Established an -Hodge decomposition theorem for Rumin's forms on sub-Riemannian contact manifolds.
New example disproves complex contact theory for fat distributions with Reeb directions.
problem Whether fat -distributions with Reeb directions always come from complex contact structures.
method Constructed a counterexample of a fat distribution with two Reeb directions that does not support a complex contact structure.
result The space of complex-contact germs has infinite codimension within the space of fat -distribution germs with Reeb directions.
We give simple characterizations of contact 1-forms in terms of Dirac structures. We also relate normal almost contact structures to the theory of Dirac structures.
The paper studies a new structure on contact manifolds and its foliation properties.
problem Investigating a new structure on contact manifolds.
method Examining weak nearly Sasakian structures and their foliations.
result The weak nearly Sasakian structure foliates into two types of totally geodesic foliations.
In this paper we produce several new invariants for CR and contact manifolds by looking at the noncommutative residue traces of various geometric projections. In the CR setting these operators arise from the Kohn-Rossi complex and include the Szegö projections on forms. In the contact setting they stem from the general…
Proves LeBrun-Salamon Conjecture for low-dimensional contact manifolds.
problem Proving the LeBrun-Salamon Conjecture in low dimensions for contact manifolds.
method Study of algebraic torus actions and use of Bialynicki-Birula decomposition and equivariant Riemann-Roch theorems.
result Contact Fano manifolds of dimension at most 9 with reductive automorphism group are homogeneous.
The paper characterizes Sasakian manifolds using weak nearly Sasakian structures.
problem Characterizing Sasakian manifolds using a new structure.
method Study of weak nearly Sasakian structures and proving theorems.
result Provides a new criterion for a weak almost contact metric manifold to be Sasakian.
Two rigidity results for Legendrian singularities in complex-analytic category.
problem Understanding singularities of Legendrian subvarieties in contact manifolds.
method Using the relation between infinitesimal contactomorphisms and holomorphic sections of the natural line bundle.
result Normal Legendrian singularities are deformation-rigid.
Contact Riemannian manifolds, with not necessarily integrable complex structures, are the generalization of pseudohermitian manifolds in CR geometry. The Tanaka-Webster-Tanno connection on such a manifold plays the role of Tanaka-Webster connection in the pseudohermitian case. We prove the contact Riemannian version of…
Study harmonicity of normal almost contact structures on Riemannian manifolds.
problem Understanding harmonicity of normal almost contact structures.
method Analyzing harmonicity through associated sections of a twistor bundle and rewriting equations in terms of curvature tensor.
result Conditions relating harmonicity of almost contact metric and almost complex structures.
In this paper we obtain the structure equation of a contact-complex Riemannian submersion and give some applications of this equation in the study of almost cosymplectic manifolds with Kaehler fibres.