Journal ArticleDOI
On k-contact einstein manifolds
Uday Chand De,Krishanu Mandal +1 more
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In this paper, K-contact Einstein manifolds satisfying the conditions RC = Q(S,C), where S is the Ricci tensor and C is the conformal curvature tensor were investigated.Abstract:
In this paper, we investigate K-contact Einstein manifolds satisfying the conditions RC = Q(S,C), where C is the conformal curvature tensor and R the Riemannian curvature tensor. Next we consider K-contact Einstein manifolds satisfying the curvature condition C.S = 0, where S is the Ricci tensor. Also we study K-contact Einstein manifolds satisfying the condition S.C = 0. Finally, we consider K-contact Einstein manifolds satisfying Z .C = 0, where Z is the concircular curvature tensor.read more
Citations
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Generalized Ricci Solitons on K-contact manifolds
TL;DR: In this article, it was shown that a K-contact manifold admitting generalised Ricci solitons is an Einstein one, and it was further shown that such a manifold is an Euler manifold.
Journal ArticleDOI
Conformal Equitorsion and Concircular Transformations in a Generalized Riemannian Space
TL;DR: For every five independent curvature tensors in Generalized Riemannian space, the above transformations are investigated and corresponding invariants-5 concircular tensors of concircularity transformations are found as discussed by the authors.
Journal Article
Some Curvature Properties on Sasakian Manifolds
Abhishek Kushwaha,Dhruwa Narain +1 more
TL;DR: In this article, the authors studied projective curvature tensors in a sasakian manifold and proved that projective tensors are identical to curvatures tensors of SIFT.
Journal ArticleDOI
$w_{2}$-curvature tensor on k-contact manifolds
TL;DR: In this paper, the authors obtained sufficient conditions for a K-contact manifold to be a Sasakian manifold, which is the case for the case of the K contact manifold in this paper.
References
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Journal ArticleDOI
Structure theorems on riemannian spaces satisfying R(X, Y) · R =0,
TL;DR: In this paper, Tanno et al. showed that the curvature tensor R of a locally symmetric Riemannian space satisfies R(X, Y) R − 0 for all tangent vectors X and 7, where the linear endomorphism R(x, y) acts on R as a derivation.
Book ChapterDOI
Conformal Transformations between Einstein Spaces
TL;DR: In this paper, the authors present a solution to the question "When can an Einstein space be mapped conformally on some (possibly different) Einstein space and in how many ways can it be so mapped?" The answer is given in terms of local coordinates.
Book
Inversion theory and conformal mapping
TL;DR: Inversion theory in the plane Linear fractional transformations Advanced calculus and conformal maps Conformal maps in Euclidean space The classical proof of Liouville's theorem When does inversion preserve convexity? as discussed by the authors.
Journal ArticleDOI
Einstein manifolds and contact geometry
TL;DR: In this article, it was shown that every K-contact Einstein manifold is SasakianEinstein and several corollaries of this result were discussed, e.g., the relation between the two manifold types.