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Integral formulas in riemannian geometry
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This article is published in Bulletin of The London Mathematical Society.The article was published on 1973-03-01. It has received 331 citations till now. The article focuses on the topics: Riemannian geometry & Fundamental theorem of Riemannian geometry.read more
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Isometric immersion of a compact riemannian manifold into a euclidean space
TL;DR: In this article, it was shown that an isometric immersion of an n−dimensional compact Riemannian manifold of non-negative Ricci curvature with scalar curvature always less than n(n−1)λ−2 into a Euclidean space of dimension n + 1 can not be contained in a ball of radius λ.
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Certain types of metrics on almost coKähler manifolds
TL;DR: In this article, it was shown that Bach flat almost coKahler manifold admits Ricci solitons, satisfying the critical point equation (CPE) or Bach flat.
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Evolution of Surfaces and the Kinematics of Membranes
TL;DR: In this paper, the polar decomposition theorem for a two-dimensional membrane is used to produce a set of equations that describe the evolution of the geometrical quantities of a moving surface, i.e., the metric, the unit normal, the shape operator, second fundamental form, the mean and the Gauss curvature.
Some global properties of pseudo-cyclic Ricci symmetric manifolds
TL;DR: In this article, it was shown that in a compact, orientable pseudo cyclic Ricci symmetric manifold without boundary, there exists no non-zero Killing (resp., projective Killing, con- formal Killing) vector fleld, and also it was proved that in such a manifold a harmonic vector Fleld reduces to a parallel Fleld.