scholarly journals Classification of Ricci semisymmetric contact metric manifolds

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2527-2535
Author(s):  
Pradip Majhi ◽  
Uday De
Keyword(s):  
Curvature Tensor ◽  
Second Order ◽  
Curvature Condition ◽  
Ricci Operator ◽  
Contact Metric Manifolds ◽  
Order Parallel ◽  
Symmetric Properties

The object of the present paper is to study Ricci semisymmetric contact metric manifolds. As a consequence of the main result we deduce some important corollaries. Besides these we study contact metric manifolds satisfying the curvature condition Q,R = 0, where Q and R denote the Ricci operator and curvature tensor respectively. Also we study the symmetric properties of a second order parallel tensor in contact metric manifolds. Finally, we give an example to verify the main result.

Some curvature properties of paracontact metric manifolds

2018 ◽  
Vol 9 (3) ◽  
pp. 159-165
Author(s):  
Krishanu Mandal ◽  
Uday Chand De
Keyword(s):  
Sectional Curvature ◽  
Curvature Tensor ◽  
Second Order ◽  
Plane Section ◽  
Riemannian Curvature ◽  
Curvature Condition ◽  
Ricci Operator ◽  
Riemannian Curvature Tensor

AbstractThe purpose of this paper is to study Ricci semisymmetric paracontact metric manifolds satisfying{\nabla_{\xi}h=0}and such that the sectional curvature of the plane section containing ξ equals a non-zero constantc. Also, we study paracontact metric manifolds satisfying the curvature condition{Q\cdot R=0}, whereQandRare the Ricci operator and the Riemannian curvature tensor, respectively, and second order symmetric parallel tensors in paracontact metric manifolds under the same conditions. Several consequences of these results are discussed.

scholarly journals Some characterizations of three-dimensional trans-Sasakian manifolds admitting η- Ricci solitons and trans-Sasakian manifolds as Kagan subprojective space

2020 ◽  
Vol 72 (3) ◽  
pp. 427-432
Author(s):  
A. Sarkar ◽  
A. Sil ◽  
A. K. Paul
Keyword(s):  
Curvature Tensor ◽  
Ricci Tensor ◽  
Three Dimensional ◽  
Ricci Soliton ◽  
Second Order ◽  
Ricci Solitons ◽  
Riemann Curvature ◽  
Sasakian Manifolds ◽  
Riemann Curvature Tensor ◽  
Order Parallel

UDC 514.7 The object of the present paper is to study three-dimensional trans-Sasakian manifolds admitting η -Ricci soliton. Actually, we study such manifolds whose Ricci tensor satisfy some special conditions like cyclic parallelity, Ricci semisymmetry, ϕ -Ricci semisymmetry, after reviewing the properties of second order parallel tensors on such manifolds. We determine the form of Riemann curvature tensor of trans-Sasakian manifolds of dimension greater than three as Kagan subprojective spaces. We also give some classification results of trans-Sasakian manifolds of dimension greater than three as Kagan subprojective spaces.

scholarly journals Quarter-Symmetric Nonmetric Connection on P-Sasakian Manifolds

ISRN Geometry ◽  
2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Abul Kalam Mondal ◽  
U. C. De
Keyword(s):  
Curvature Tensor ◽  
Sasakian Manifold ◽  
Second Order ◽  
Sasakian Manifolds ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Metric Connection ◽  
Concircular Curvature Tensor ◽  
Order Parallel

The object of the present paper is to study a quarter-symmetric nonmetric connection on a P-Sasakian manifold. In this paper we consider the concircular curvature tensor and conformal curvature tensor on a P-Sasakian manifold with respect to the quarter-symmetric nonmetric connection. Next we consider second-order parallel tensor with respect to the quarter-symmetric non-metric connection. Finally we consider submanifolds of an almost paracontact manifold with respect to a quarter-symmetric non-metric connection.

SATANIC AND THELEMIC CIRCLES ON KNOTS

2013 ◽  
Vol 22 (05) ◽  
pp. 1350017 ◽  
Author(s):  
G. FLOWERS
Keyword(s):  
Geometric Interpretation ◽  
Second Order ◽  
Geometric Properties ◽  
Vassiliev Invariants ◽  
Vassiliev Invariant ◽  
Knot Diagrams

While Vassiliev invariants have proved to be a useful tool in the classification of knots, they are frequently defined through knot diagrams, and fail to illuminate any significant geometric properties the knots themselves may possess. Here, we provide a geometric interpretation of the second-order Vassiliev invariant by examining five-point cocircularities of knots, extending some of the results obtained in [R. Budney, J. Conant, K. P. Scannell and D. Sinha, New perspectives on self-linking, Adv. Math. 191(1) (2005) 78–113]. Additionally, an analysis on the behavior of other cocircularities on knots is given.

scholarly journals The curvature tensor of $$(\kappa ,\mu ,\nu )$$ ( κ , μ , ν ) -contact metric manifolds

2015 ◽  
Vol 177 (3) ◽  
pp. 331-344
Author(s):  
Kadri Arslan ◽  
Alfonso Carriazo ◽  
Verónica Martín-Molina ◽  
Cengizhan Murathan
Keyword(s):  
Curvature Tensor ◽  
Contact Metric Manifolds

A classification of second-order technical progress operators

1984 ◽  
Vol 14 (2-3) ◽  
pp. 269-274 ◽  
Author(s):  
Joel D. Scheraga
Keyword(s):  
Technical Progress ◽  
Second Order

Lie group classification of second-order ordinary difference equations

2000 ◽  
Vol 41 (1) ◽  
pp. 480-504 ◽  
Author(s):  
Vladimir Dorodnitsyn ◽  
Roman Kozlov ◽  
Pavel Winternitz
Keyword(s):  
Lie Group ◽  
Difference Equations ◽  
Group Classification ◽  
Second Order ◽  
Lie Group Classification
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