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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Gradient Ricci Solitons With A Conformal Vector Field, Ramesh Sharma
Gradient Ricci Solitons With A Conformal Vector Field, Ramesh Sharma
Mathematics Faculty Publications
We show that a connected gradient Ricci soliton (M,g,f,λ) with constant scalar curvature and admitting a non-homothetic conformal vector field V leaving the potential vector field invariant, is Einstein and the potential function f is constant. For locally conformally flat case and non-homothetic V we show without constant scalar curvature assumption, that f is constant and g has constant curvature.
Almost Ricci Solitons And K-Contact Geometry, Ramesh Sharma
Almost Ricci Solitons And K-Contact Geometry, Ramesh Sharma
Mathematics Faculty Publications
We give a short Lie-derivative theoretic proof of the following recent result of Barros et al. “A compact non-trivial almost Ricci soliton with constant scalar curvature is gradient, and isometric to a Euclidean sphere”. Next, we obtain the result: a complete almost Ricci soliton whose metric g is K-contact and flow vector field X is contact, becomes a Ricci soliton with constant scalar curvature. In particular, for X strict, g becomes compact Sasakian Einstein.
Contact Hypersurfaces Of A Bochner-Kaehler Manifold, Amalendu Ghosh, Ramesh Sharma
Contact Hypersurfaces Of A Bochner-Kaehler Manifold, Amalendu Ghosh, Ramesh Sharma
Mathematics Faculty Publications
We have studied contact metric hypersurfaces of a Bochner-Kaehler manifold and obtained the following two results: (1) A contact metric constant mean curvature (C M C) hypersurface of a Bochner-Kaehler manifold is a (k, µ)-contact manifold, and (2) If M is a compact contact metric C M C hypersurface of a Bochner-Kaehler manifold with a conformal vector field V that is neither tangential nor normal anywhere, then it is totally umbilical and Sasakian, and under certain conditions on V , is isometric to a unit sphere.
Conformal Classification Of (K, Μ)-Contact Manifolds, Ramesh Sharma, Luc Vrancken
Conformal Classification Of (K, Μ)-Contact Manifolds, Ramesh Sharma, Luc Vrancken
Mathematics Faculty Publications
First we improve a result of Tanno that says "If a conformal vector field on a contact metric manifold M is a strictly infinitesimal contact transformation, then it is an infinitesimal automorphism of M" by waiving the "strictness" in the hypothesis. Next, we prove that a (k, μ)-contact manifold admitting a non-Killing conformal vector field is either Sasakian or has k = –n – 1, μ = 1 in dimension > 3; and Sasakian or flat in dimension 3. In particular, we show that (i) among all compact simply connected (k, μ)-contact manifolds of dimension > 3, only the unit sphere S2n+1 …