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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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Locally ϕ-Symmetric Generalized Sasakian-Space Forms
A. Sarkar,M. Sen +1 more
TL;DR: In this paper, the authors find necessary and sufficient conditions for locally ϕ-symmetric generalized Sasakian-space forms to have constant scalar curvature, η -parallel Ricci tensor, and cyclic parallel R tensor.
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Aspects of globally-stable tracking for certain classes of simple mechanical systems
Aradhana Nayak,Ravi N. Banavar +1 more
TL;DR: This paper addresses the almost-global tracking problem for an SMS on a compact Riemannian manifold embedded in Euclidean space by explicitly introducing the error dynamics.
Harmonic-Killing vector fields on Kähler manifolds
Abstract: In a previous paper we have considered the harmonicity of local infinitesimal transformations associated to a vector field on a (pseudo)-Riemannian manifold to characterise intrinsically a class of vector fields that we have called harmonic-Killing vector fields. In this paper we extend this study to other properties, such as the pluriharmonicity and the α-pluriharmonicity (α harmonic 2-form) of the local infinitesimal transformations, obtaining characterisations of these kinds of vector fields. 2000 Mathematics Subject Classification 53C43, 53C55, 53B20
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A remark on the Laplacian operator which acts on symmetric tensors
TL;DR: In this paper, it was shown that the Yano rough Laplacian is the equivalent of the Hodge-de-Rham LaplACian on a compact Riemannian manifold.
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Intrinsic Theory of Projective Changes in Finsler Geometry
TL;DR: In this paper, the authors provide an intrinsic investigation of projective changes in Finlser geometry, following the pullback formalism, and derive intrinsic properties of the fundamental projectively invariant tensors, namely, the projective deviation tensor, the Weyl torsion tensor and the Douglas tensor.