Author
Uday De Chand
Bio: Uday De Chand is an academic researcher from University of Calcutta. The author has contributed to research in topics: Ricci curvature & Manifold. The author has an hindex of 3, co-authored 8 publications receiving 25 citations.
Papers
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TL;DR: In this paper, a new type of curvature tensor called H-curvature tensors of type (1, 3) was introduced, which is a linear combination of conformal and projective curvatures.
Abstract: In this paper, we introduce a new type of curvature tensor named H-curvature
tensor of type (1, 3) which is a linear combination of conformal and
projective curvature tensors. First we deduce some basic geometric
properties of H-curvature tensor. It is shown that a H-flat Lorentzian
manifold is an almost product manifold. Then we study pseudo H-symmetric
manifolds (PHS)n (n > 3) which recovers some known structures on Lorentzian
manifolds. Also, we provide several interesting results. Among others, we
prove that if an Einstein (PHS)n is a pseudosymmetric (PS)n, then the scalar
curvature of the manifold vanishes and conversely. Moreover, we deal with
pseudo H-symmetric perfect fluid spacetimes and obtain several interesting
results. Also, we present some results of the spacetime satisfying
divergence free H-curvature tensor. Finally, we construct a non-trivial
Lorentzian metric of (PHS)4.
8 citations
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TL;DR: In this article, a semisymmetric metric connection on a Riemannian manifold whose torsion tensor is almost pseudo symmetric was studied, and the associated 1-form of the connection on the almost pseudo-symmetric manifold was derived.
Abstract: We study a type of semisymmetric metric connection on a Riemannian manifold
whose torsion tensor is almost pseudo symmetric and the associated 1-form of
almost pseudo symmetric manifold is equal to the associated 1-form of the
semisymmetric metric connection.
6 citations
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TL;DR: In this article, it was shown that the Ricci soliton of an almost Kenmotsu manifold with conformal Reeb foliation is an Einstein metric and Ricci is expanding with λ = 4n.
Abstract: If the metric of an almost Kenmotsu manifold with conformal Reeb foliation is
a gradient Ricci soliton, then it is an Einstein metric and the Ricci
soliton is expanding. Moreover, let (M2n+1,Φ,ξ,η,g) be an almost
Kenmotsu manifold with ξ belonging to the (k,μ)′-nullity distribution and h
h≠0. If the metric g of M2n+1 is a gradient Ricci soliton, then M2n+1 is
locally isometric to the Riemannian product of an (n+1)-dimensional manifold
of constant sectional curvature -4 and a at n-dimensional manifold, also,
the Ricci soliton is expanding with λ = 4n.
5 citations
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TL;DR: In this article, the authors characterize Ricci semisymmetric almost Kenmotsu manifolds with their characteristic vector field belonging to the (k,\mu )^{`}-nullity distribution.
Abstract: The object of the present paper is to characterize Ricci semisymmetric almost Kenmotsu manifolds with its characteristic vector field \xi belonging to the (k,\mu )^{`}-nullity distribution and (k,\mu )-nullity distribution respectively. Finally, an illustrative example is given.
5 citations
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TL;DR: In this paper, the authors studied biharmonic Legendre curves, locally φ-symmetric Legendre curve and slant curve in 3-dimensional Kenmotsu manifold.
Abstract: The object of the present paper is to study biharmonic Legendre curves, locally φ-symmetric Legendre curves and slant curves in 3-dimensional Kenmotsu manifolds admitting semisymmetric metric connection. Finally, we construct an example of a Legendre curve in a 3-dimensional Kenmotsu manifold.
2 citations
Cited by
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01 Jan 1985
278 citations
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TL;DR: In this paper, the authors provide a fairly concise introduction to the basic mathematical concepts of the general theory of relativity and their applications, at a level suitable for postgraduate students, covering Riemannian geometry and Einstein's theory of gravitation, gravitational waves, the classification of exact solutions of the Einstein equations, black holes and cosmology.
Abstract: Hans Stephani 1982 Cambridge: Cambridge University Press xvi + 298 pp price £25 This textbook provides a fairly concise introduction to the basic mathematical concepts of the general theory of relativity and their applications, at a level suitable for postgraduate students. It covers Riemannian geometry and Einstein's theory of gravitation, gravitational waves, the classification of exact solutions of the Einstein equations, black holes and cosmology.
78 citations
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TL;DR: The Ricci-flat Ricci solitons with the potential vector fields pointwise collinear with the Reeb vector fields on K-almost coKahler manifolds were studied in this article.
Abstract: Let M be a compact almost coKahler manifold. If the metric g of M is a Ricci soliton and the potential vector field is pointwise collinear with the Reeb vector field, then we prove that M is Ricci-flat and coKahler and the soliton g is steady. This generalizes a Goldberg-like conjecture for coKahler manifolds obtained by Cappelletti-Montano and Pastore, namely any compact Einstein K-almost coKahler manifold is coKahler. Without the assumption of compactness, Ricci solitons with the potential vector fields pointwise collinear with the Reeb vector fields on K-almost coKahler manifolds are also studied. Moreover, we prove that there exist no gradient Ricci solitons on proper \({(\kappa, \mu)}\)-almost coKahler manifolds.
27 citations