scholarly journals On W0 and W2 ø-Symmetric Contact Manifold Admitting Quarter-Symmetric Metric Connection

2021 ◽  
Vol 2070 (1) ◽  
pp. 012075
Author(s):  
K. T. Pradeep Kumar ◽  
B.M. Roopa ◽  
K.H. Arun Kumar
Keyword(s):  
Curvature Tensor ◽  
Contact Manifold ◽  
Contact Manifolds ◽  
Metric Connection

Abstract The paper deals locally W0 and W2 curvature tensor of ø-symmetric K-contact manifolds with quarter-symmetric metric connection and some results are obtained.

scholarly journals Metric f-Contact Manifolds Satisfying the (κ, μ)-Nullity Condition

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 891
Author(s):  
Alfonso Carriazo ◽  
Luis M. Fernández ◽  
Eugenia Loiudice
Keyword(s):  
Explicit Expression ◽  
Sectional Curvature ◽  
Curvature Tensor ◽  
Tensor Field ◽  
Contact Manifold ◽  
Contact Manifolds

We prove that if the f-sectional curvature at any point of a ( 2 n + s ) -dimensional metric f-contact manifold satisfying the ( κ , μ ) nullity condition with n > 1 is independent of the f-section at the point, then it is constant on the manifold. Moreover, we also prove that a non-normal metric f-contact manifold satisfying the ( κ , μ ) nullity condition is of constant f-sectional curvature if and only if μ = κ + 1 and we give an explicit expression for the curvature tensor field in such a case. Finally, we present some examples.

scholarly journals $W_{2}$-CURVATURE TENSOR ON K-CONTACT MANIFOLDS

2021 ◽  
pp. 995
Author(s):  
Krishnendu De
Keyword(s):  
Curvature Tensor ◽  
Sufficient Conditions ◽  
Contact Manifold ◽  
Sasakian Manifold ◽  
Contact Manifolds

The object of the present paper is to obtain sufficient conditions  for a K-contact manifold to be a Sasakian manifold.

scholarly journals Open books and exact symplectic cobordisms

2018 ◽  
Vol 29 (04) ◽  
pp. 1850026 ◽  
Author(s):  
Mirko Klukas
Keyword(s):  
Disjoint Union ◽  
Contact Manifold ◽  
Higher Dimensions ◽  
Fiber Bundles ◽  
Open Book ◽  
Contact Manifolds ◽  
Open Books ◽  
Symplectic Cobordism ◽  
The Given ◽  
Symplectic Cobordisms

Given two open books with equal pages, we show the existence of an exact symplectic cobordism whose negative end equals the disjoint union of the contact manifolds associated to the given open books, and whose positive end induces the contact manifold associated to the open book with the same page and concatenated monodromy. Using similar methods, we show the existence of strong fillings for contact manifolds associated with doubled open books, a certain class of fiber bundles over the circle obtained by performing the binding sum of two open books with equal pages and inverse monodromies. From this we conclude, following an outline by Wendl, that the complement of the binding of an open book cannot contain any local filling obstruction. Given a contact [Formula: see text]-manifold, according to Eliashberg there is a symplectic cobordism to a fibration over the circle with symplectic fibers. We extend this result to higher dimensions recovering a recent result by Dörner–Geiges–Zehmisch. Our cobordisms can also be thought of as the result of the attachment of a generalized symplectic [Formula: see text]-handle.

scholarly journals NATURAL CONNECTION WITH TOTALLY SKEW-SYMMETRIC TORSION ON ALMOST CONTACT MANIFOLDS WITH B-METRIC

2012 ◽  
Vol 09 (05) ◽  
pp. 1250044 ◽  
Author(s):  
MANCHO MANEV
Keyword(s):  
Curvature Tensor ◽  
Torsion Tensor ◽  
Contact Manifolds ◽  
Natural Connection ◽  
Civita Connection ◽  
Levi Civita Connection

A natural connection with totally skew-symmetric torsion on almost contact manifolds with B-metric is constructed. The class of these manifolds, where the considered connection exists, is determined. Some curvature properties for this connection, when the corresponding curvature tensor has the properties of the curvature tensor for the Levi-Civita connection and the torsion tensor is parallel, are obtained.

scholarly journals Certain results on generalized (k,\mu)-contact manifolds

2017 ◽  
Vol 37 (3) ◽  
pp. 131
Author(s):  
Pradip Majhi ◽  
Gopal Ghosh
Keyword(s):  
Contact Manifold ◽  
Contact Manifolds

The object of the present paper is to study generalized (k,\mu)-contact manifolds. At first we consider \phi-semisymmetric generalized (k,\mu)-contact manifolds. Beside these we study extended pseudo projective at generalized (k,\mu)-contact manifolds. Also (k,\mu )-contact manifold satisfying \barP^e.S = 0 is also considered. As a consequence we obtain several corollaries.

scholarly journals Space time manifolds and contact structures

1990 ◽  
Vol 13 (3) ◽  
pp. 545-553 ◽  
Author(s):  
K. L. Duggal
Keyword(s):  
Contact Structure ◽  
Contact Manifold ◽  
Contact Structures ◽  
Timelike Vector ◽  
Contact Manifolds ◽  
New Class ◽  
Dimensional Spacetime ◽  
Globally Hyperbolic Spacetimes ◽  
Hyperbolic Spacetimes ◽  
Regular Contact

A new class of contact manifolds (carring a global non-vanishing timelike vector field) is introduced to establish a relation between spacetime manifolds and contact structures. We show that odd dimensional strongly causal (in particular, globally hyperbolic) spacetimes can carry a regular contact structure. As examples, we present a causal spacetime with a non regular contact structure and a physical model [Gödel Universe] of Homogeneous contact manifold. Finally, we construct a model of 4-dimensional spacetime of general relativity as a contact CR-submanifold.

scholarly journals Translated points on hypertight contact manifolds

2018 ◽  
Vol 10 (02) ◽  
pp. 289-322
Author(s):  
Matthias Meiwes ◽  
Kathrin Naef
Keyword(s):  
Floer Homology ◽  
Contact Manifold ◽  
Contact Form ◽  
Contact Manifolds ◽  
Rabinowitz Floer Homology

A contact manifold admitting a supporting contact form without contractible Reeb orbits is called hypertight. In this paper we construct a Rabinowitz–Floer homology associated to an arbitrary supporting contact form for a hypertight contact manifold [Formula: see text], and use this to prove versions of a conjecture of Sandon [17] on the existence of translated points and to show that positive loops of contactomorphisms give rise to non-contractible Reeb orbits.

scholarly journals On Sectional Curvature of Metric Connection with Vectorial Torsion

2020 ◽  
pp. 124-127
Author(s):  
E.D. Rodionov ◽  
V.V. Slavsky ◽  
O.P. Khromova
Keyword(s):  
Sectional Curvature ◽  
Curvature Tensor ◽  
Sufficient Conditions ◽  
Civita Connection ◽  
Modern Physics ◽  
Metric Connection ◽  
Levi Civita Connection ◽  
The Difference ◽  
Topology Of Manifolds ◽  
Conformal Deformations

Papers of many mathematicians are devoted to the study of semisymmetric connections or metric connections with vector torsion on Riemannian manifolds. This type of connectivity is one of the three main types discovered by E. Cartan and finds its application in modern physics, geometry, and topology of manifolds. Geodesic lines and the curvature tensor of a given connection were studied by I. Agricola, K. Yano, and other mathematicians. In particular, K. Yano proved an important theorem on the connection of conformal deformations and metric connections with vector torsion. Namely: a Riemannian manifold admits a metric connection with vector torsion and the curvature tensor being equal to zero if and only if it is conformally flat. Although the curvature tensor of a hemisymmetric connection has a smaller number of symmetries compared to the Levi-Civita connection, it is still possible to define the concept of sectional curvature in this case. The question naturally arises about the difference between the sectional curvature of a semisymmetric connection and the sectional curvature of a Levi-Civita connection.This paper is devoted to the study of this issue, and the authors find the necessary and sufficient conditions for the sectional curvature of the semisymmetric connection to coincide with the sectional curvature of the Levi-Civita connection. Non-trivial examples of hemisymmetric connections are constructed when possible.

scholarly journals Two closed orbits for non-degenerate Reeb flows

2020 ◽  
pp. 1-36
Author(s):  
MIGUEL ABREU ◽  
JEAN GUTT ◽  
JUNGSOO KANG ◽  
LEONARDO MACARINI
Keyword(s):  
Contact Manifold ◽  
Contact Manifolds ◽  
Symplectic Homology ◽  
Connected Sums ◽  
Reeb Flows ◽  
Closed Orbits ◽  
Finite Quotient ◽  
Closed Contact ◽  
First Chern Class ◽  
Toric Contact Manifolds

Abstract We prove that every non-degenerate Reeb flow on a closed contact manifold M admitting a strong symplectic filling W with vanishing first Chern class carries at least two geometrically distinct closed orbits provided that the positive equivariant symplectic homology of W satisfies a mild condition. Under further assumptions, we establish the existence of two geometrically distinct closed orbits on any contact finite quotient of M. Several examples of such contact manifolds are provided, like displaceable ones, unit cosphere bundles, prequantisation circle bundles, Brieskorn spheres and toric contact manifolds. We also show that this condition on the equivariant symplectic homology is preserved by boundary connected sums of Liouville domains. As a byproduct of one of our applications, we prove a sort of Lusternik–Fet theorem for Reeb flows on the unit cosphere bundle of not rationally aspherical manifolds satisfying suitable additional assumptions.

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