The author is planning if possible classify all three-dimensional -manifolds wether contact metric, almost cosymplectic, para-contact metric, almost para-cosymplectic. Of course classification in contact or almost cosymplectic cases already is provdied. Up to authors knowledge there is no classification for para…
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48 results for “para-contact metric manifolds”
The Schouten-van Kampen affine connection adapted to an almost (para) contact metric structuremath.DG
We study the Schouten-van Kampen connection associated to an almost contact or paracontact metric structure. With the help of such a connection, some classes of almost (para) contact metric manifolds are characterized. Certain curvature properties of this connection are found.
In monograph of D. E. Blair "Riemannian geometry of contact and symplectic manifolds" and in the paper of S. Zamkovoy "Canonical connections on paracontact manifolds", the curvature identities respectively for contact and paracontact metric manifold are proved. We obtain the curvature identity in the wider class of man…
Study on structures and almost para-contact structures in 7D.
problem Understanding the relation between structures and almost para-contact structures.
method Calculating projections using properties of structures.
result Determined the class of almost para-contact structures induced by structures.
In this paper, we introduce generalized almost para-contact manifolds and obtain normality conditions in terms of classical tensor fields. We show that such manifolds naturally carry certain Lie bialgebroid/quasi-Lie algebroid structures on them and we relate this new generalized manifolds with classical almost para-co…
It is established that the existence of non-isotropic vector field which Jacobi operator of maximal rank is an obstacle for the existence of non-trivial second-order symmetric parallel tensor field. In turns out that presence of such obstacle follows that manifold as pseudo-Riemannian manifold is locally non-reducible.…
Paper introduces new hypersurface types on statistical manifolds.
problem Understanding new hypersurface types on statistical manifolds.
method Introducing and analyzing new classes of hypersurfaces.
result Obtained properties and relations on specific hypersurface types.
Unified framework for rigidity results on -manifolds.
problem Rigidity of metrics on -manifolds.
method Study of deviations preserving bi-Legendrian structure, orthogonalizing canonical structure.
result Unified rigidity results in both Riemannian and semi-Riemannian categories.
The study explores δ-almost gradient Yamabe solitons on pseudo-Riemannian manifolds.
problem Characterizing δ-almost gradient Yamabe solitons on pseudo-Riemannian manifolds.
method Analyzing δ-almost Yamabe solitons within the framework of para-contact metric manifolds, proving properties and conditions for solitons.
result Characterization of δ-almost gradient Yamabe solitons on K-paracontact metric manifolds.
On the classification of left-invariant para-Kähler structures on four-dimensional Lie groupsmath.DG
The paper classifies para-Kähler structures on Lie groups.
problem Classifying para-Kähler structures on Lie groups.
method Classification based on symplectic Lie algebras, finding compatible para-complex structures and pseudo-Riemannian metrics.
result Explicit forms of para-complex structures and pseudo-Riemannian metrics are found.
The paper classifies 3D paracontact and almost paracosymplectic spaces.
problem Classifying 3D paracontact and almost paracosymplectic spaces.
method Detailed structure analysis and local classification for all possible values of κ.
result Local classification of paracontact metric and almost paracosymplectic (κ,μ)-spaces for every possible value of κ.
New contact structures extend supergravity solutions.
problem Extend supergravity solutions using new contact structures.
method Introduce and investigate -contact metric structures, focusing on null contact structures.
result Appropriate direct products of -Einstein structures produce solutions of six-dimensional minimal supergravity.
Contact metric three manifolds and Lorentzian geometry with torsion in six-dimensional supergravitymath.DG
We introduce the notion of -Einstein -contact metric three-manifold, which includes as particular cases -Einstein Riemannian and Lorentzian (para) contact metric three-manifolds, but which in addition allows for the Reeb vector field to be null. We prove that the product of an $\vare…
A curvature-type tensor invariant called para contact (pc) conformal curvature is defined on a paracontact manifold. It is shown that a paracontact manifold is locally paracontact conformal to the hyperbolic Heisenberg group or to a hyperquadric of neutral signature if and only if the pc conformal curvature vanishes. I…
Local flatness theorem for paraquaternionic contact structures.
problem Local flatness of paraquaternionic contact manifolds.
method Defined paraquaternionic contact conformal curvature tensor and showed local flatness condition.
result Paraquaternionic contact conformal curvature vanishing implies local flatness.
Unified framework for classifying Sasakian, K-contact, and (κ, μ)-manifolds.
problem Classifying and understanding different types of contact metric manifolds.
method Investigating metric structures on symplectizations and proving the existence of a unique metric symplectization.
result Unified framework for classifying Sasakian, K-contact, and (κ, μ)-manifolds.
We give a characterization of a contact metric manifold as a special almost contact metric manifold and discuss an almost contact metric manifold which is {a} natural generalization of the contact metric manifolds introduced by Y. Tashiro.
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 prove that the L^2 Riemannian metric on the manifold of all smooth Riemannian metrics on a fixed closed, finite-dimensional manifold induces a metric space structure. As the L^2 metric is a weak Riemannian metric, this fact does not follow from general results. In addition, we prove several results on the exponentia…
The paper embeds CR manifolds into twistor spaces and constructs neutral hyperkähler metrics.
problem Embedding CR manifolds into twistor spaces and constructing neutral hyperkähler metrics.
method Embedding a real analytic twistor CR manifold into the twistor space of a Poincaré-Einstein metric, constructing the associated Fefferman ambient metric as a neutral hyperkähler metric.
result The construction of neutral hyperkähler metrics associated with twistor CR manifolds.
Diagonalizes metrics of 3D Lorentzian manifolds.
problem Diagonalizing metrics of 3D Lorentzian manifolds.
method Applying the technique of moving frames.
result Every smooth Lorentzian 3-manifold admits an atlas with a diagonal metric.
The paper defines -normality for contact and paracontact manifolds and explores their properties.
problem Defining and characterizing -normality for contact and paracontact manifolds.
method Using the Levi-Civita covariant derivative and Tanaka-like connections.
result Existence and uniqueness of connections on -normal manifolds.
New Einstein metrics found on complex manifolds.
problem Locally symmetric metrics on complex manifolds.
method Construction of manifolds with specific curvature properties.
result Infinitely many manifolds with negatively curved Einstein metrics but no locally symmetric metrics.
Classifies Einstein metrics on 4-manifolds with specific symmetry groups.
problem Classifying Einstein metrics on 4-manifolds with certain symmetry properties.
method Analyzes cohomogeneity-one Einstein metrics and uses symmetry properties.
result Locally symmetric or homothetic to the Page metric on .
The paper studies Ricci solitons on contact pseudo-metric manifolds and their properties.
problem Characterizing properties of contact pseudo-metric manifolds with Ricci solitons.
method Analyzing specific types of Ricci solitons on Sasakian and contact pseudo-metric manifolds.
result Properties of Ricci solitons on contact pseudo-metric manifolds, leading to Einstein manifolds under certain conditions.
Researchers compute curvatures of Stiefel manifolds with new metrics.
problem Computing curvatures of Stiefel manifolds with specific metrics.
method Two approaches: global curvature formula and left-invariant metrics.
result Stiefel manifolds always carry an Einstein metric and have non-negative sectional curvature.
Characterizes self-isometries of Riemannian metrics on compact manifolds.
problem Understanding isometries of Riemannian metrics.
method Characterization of self-isometries and proof of isometry conditions.
result Two Riemannian metric spaces are isometric if and only if their manifolds are diffeomorphic.
The study explores new metric structures on manifolds, linking them to Einstein metrics.
problem Characterizing and understanding weak K-contact manifolds and their properties.
method Analyzing weak K-contact manifolds and their properties, including the parallel Ricci tensor and generalized Ricci soliton structures.
result Sufficient conditions for weak K-contact manifolds with specific properties to be Einstein manifolds.
The paper constructs a new metric on Kähler manifolds.
problem Finding metrics with specific curvature properties on Kähler manifolds.
method Constructing an almost negatively 1/4-pinched Riemannian metric.
result First known examples of not locally symmetric Kähler manifolds with this metric.
This is the author's Ph.D. thesis, submitted to the University of Leipzig. It deals with the Riemannian metric on the manifold of all smooth Riemannian metrics on a fixed closed, finite-dimensional manifold. The main body of the thesis is a description of the completion manifold of metrics with respect to the $L^…
The paper studies contact pseudo-metric manifolds with a specific curvature condition.
problem Investigating properties of contact pseudo-metric manifolds under a nullity condition.
method Introducing and analyzing -contact pseudo-metric manifolds and generalized -contact pseudo-metric manifolds.
result The curvature of these manifolds is constant if the -sectional curvature is independent of the -section.
New approach finds Kähler metrics on compact complex manifolds.
problem Finding Kähler metrics on compact complex manifolds.
method Defining a new functional whose critical points are Kähler metrics.
result Critical points of the new functional are precisely the Kähler metrics.
Eigenvalue problem for Kähler metrics on compact manifolds.
problem Eigenvalue problem for the Laplacian on Kähler manifolds.
method Introducing -extremal Kähler metrics and deducing conditions for extremality.
result Conditions for a Kähler metric to be -extremal.
The paper defines quasi-isometry for almost contact metric manifolds and explores its properties.
problem Understanding quasi-isometry in almost contact metric manifolds.
method Definition and study of quasi-isometry for almost contact metric manifolds.
result Established a relation between scalar curvature and quasi-isometric constants.
The paper studies para-Sasaki-like manifolds with a new metric connection.
problem Investigating new geometric structures on para-Sasaki-like manifolds.
method Deriving relations between connections, analyzing curvature tensors, studying solitons, constructing examples.
result Derived relations and properties of para-Sasaki-like manifolds with the generalized symmetric metric connection.
In this paper, a systematic study of Kenmotsu pseudo-metric manifolds are introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant -sectional curvature, and prove the structure theorem for -conformally fla…
Study on generalized quasi-Einstein structures in contact geometry.
problem Characterizing and understanding generalized quasi-Einstein structures in contact geometry.
method Investigation of properties, existence, and characterizations of generalized quasi-Einstein normal metric contact pair manifolds.
result Normal metric contact pair manifolds with generalized quasi-constant curvature are generalized quasi-Einstein manifolds.
Given a fixed closed manifold M, we exhibit an explicit formula for the distance function of the canonical L^2 Riemannian metric on the manifold of all smooth Riemannian metrics on M. Additionally, we examine the (metric) completion of the manifold of metrics with respect to the L^2 metric and show that there exists a …
Two lectures on metric geometry of manifolds.
problem Understanding metric geometry properties of manifolds.
method Discussion of specific inequalities and concepts.
result Exploration of metric geometry properties of manifolds.
The paper examines Einstein doubly warped product manifolds with a semi-symmetric metric connection.
problem Characterizing Einstein doubly warped product manifolds with a semi-symmetric metric connection.
method Deriving curvature formulas and proving necessary and sufficient conditions for a manifold to be a warped product.
result Obtained results for Einstein doubly warped product manifolds and Einstein-like doubly warped product manifolds.
Study on collapsing Calabi-Yau manifolds and their metrics.
problem Understanding degenerations of Calabi-Yau manifolds with Ricci-flat Kahler metrics.
method Survey of recent developments, focusing on volume collapsing metrics.
result New insights into the behavior of Calabi-Yau manifolds under volume collapse.
No Einstein metrics found on extended graph 4-manifolds.
problem Finding Einstein metrics on extended graph 4-manifolds.
method Defined and analyzed extended graph 4-manifolds as per [FLS15].
result Extended graph 4-manifolds do not support Einstein metrics.
New Kähler metrics generalize Calabi's and relate to Fano manifolds.
problem Existence of extremal Kähler metrics on Fano manifolds.
method Introducing -extremal Kähler metrics and relating them to multiplier Hermitian-Einstein metrics.
result Existence of -extremal Kähler metrics implies existence of multiplier Hermitian-Einstein metrics on Fano manifolds.
Study rough Riemannian metrics on manifolds, proving their connectedness and completeness.
problem Understanding the space of all locally elliptic and bounded Riemannian metrics on manifolds.
method Introduced an extended metric space and proved its properties.
result Proved the space of rough Riemannian metrics is complete and connected.
Uniform K-stability ensures existence of special metrics on toric manifolds.
problem Existence of conformally Kähler, Einstein-Maxwell metrics on toric manifolds.
method Introducing uniform K-stability and showing its equivalence to properness of relative K-energy.
result Uniform K-stability is necessary and sufficient for the existence of -extremal metrics on toric manifolds.
Stability of SKT metrics under deformations on complex manifolds.
problem Stability of strong Kähler with torsion metrics under small deformations.
method Finding necessary conditions for stability of SKT metrics along a family of complex manifolds.
result Necessary conditions for the stability of SKT metrics on a smooth curve of Hermitian metrics.
Study cohomological and metric properties of non-Kähler complex manifolds.
problem Understanding cohomological invariants and metrics of non-Kähler complex manifolds.
method Partial account of problems through cohomological and metric properties.
result Partial insights into cohomological and metric properties of non-Kähler manifolds.
New extremal metrics found on Kähler manifolds.
problem Constructing extremal metrics on Kähler manifolds.
method Test configurations for strictly semistable Kähler manifolds.
result Infinitely many new examples of manifolds with extremal Kähler metrics.