Topic
Scalar curvature
About: Scalar curvature is a research topic. Over the lifetime, 12701 publications have been published within this topic receiving 296040 citations. The topic is also known as: Ricci scalar.
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TL;DR: An algebraic study of the torsion and curvature of almost-Hermitian manifolds with emphasis on the space of curvature tensors orthogonal to those of Kahler metrics was made in this article.
Abstract: An algebraic study is made of the torsion and curvature of almost-Hermitian manifolds with emphasis on the space of curvature tensors orthogonal to those of Kahler metrics.
90 citations
TL;DR: In this article, the flag curvature of a Finsler metric with isotropic S-curvature is studied and the curvature is partially determined when certain non-Riemannian quantities such as Cartan torsion, Landsberg curvature and S-Curvature vanish.
Abstract: The flag curvature of a Finsler metric is called a Riemannian quantity because it is an extension of sectional curvature in Riemannian geometry. In Finsler geometry, there are several non-Riemannian quantities such as the (mean) Cartan torsion, the (mean) Landsberg curvature and the S-curvature, which all vanish for Riemannian metrics. It is important to understand the geometric meanings of these quantities. In the paper, Finsler metrics of scalar curvature (that is, the flag curvature is a scalar function on the slit tangent bundle) are studied and the flag curvature is partially determined when certain non-Riemannian quantities are isotropic. Using the obtained formula for the flag curvature, locally projectively flat Randers metrics with isotropic S-curvature are classified.
90 citations
TL;DR: In this paper, the authors studied Ricci-flat and Einstein-Lorentzian multiply warped products and applied their results to other relativistic space-times, i.e., Reissner-Nordstrom, Kasner space times, Banados-Teitelboim-Zanelli and de Sitter black hole solutions.
90 citations
TL;DR: In this paper, the authors studied the Ricci tensor invariance of the Riemannian curvature tensor of the Kenmotsu manifold, which is derived from the almost contact Ricci manifold with some special conditions.
Abstract: The purpose of this paper is to study a Kenmotsu manifold which is derived from the almost contact Riemannian manifold with some special conditions. In general, we have some relations about semi-symmetric, Ricci semi-symmetric or Weyl semisymmetric conditions in Riemannian manifolds. In this paper, we partially classify the Kenmotsu manifold and consider the manifold admitting a transformation which keeps Riemannian curvature tensor and Ricci tensor invariant.
90 citations
TL;DR: In this paper, the authors considered a complex surface M with anti-self-dual hermitian metric h and studied the holomorphic properties of its twistor space Z and showed that the naturally defined divisor line bundle [X] is isomorphic to the -1/2 power of the canonical bundle of Z if and only if there is a Kahler metric of zero scalar curvature in the conformal class of h.
Abstract: We consider a complex surface M with anti-self-dual hermitian metric h and study the holomorphic properties of its twistor space Z We show that the naturally defined divisor line bundle [X] is isomorphic to the -1/2 power of the canonical bundle of Z, if and only if there is a Kahler metric of zero scalar curvature in the conformal class of h This has strong consequences on the geometry of M, which were also found by C Boyer [3] using completely different methods We also prove the existence of a very close relation between holomorphic vector fields on M and Z in the case that M is compact and Kahler
90 citations