In this paper, we study half-lightlike submanifolds of a semi-Riemannian manifold such that the shape operator of screen distribution is conformal to the shape operator of screen transversal distribution. We mainly obtain some results concerning the induced Ricci curvature tensor and the null sectional curvature of screen transversal conformal half-lightlike submanifolds. 2010 Mathematics Subje...

In this paper, we prove that the Ricci tensor of an almost Kenmotsu 3-h-manifold is cyclic-parallel if and only if it is parallel and hence, the manifold is locally isometric to either the hyperbolic space H3(−1) or the Riemannian product H2(−4)× R. c ©2016 All rights reserved.

Purely magnetic spacetimes, in which the Riemann tensor satisfies Rabcdu b u d = 0 for some unit timelike vector u, are studied. The algebraic consequences for the Weyl and Ricci tensors are examined in detail and consideration given to the uniqueness of u. Some remarks concerning the nature of the congruence associated with u are made. ∗ Email:[email protected]

1 Contents Applications of Hamilton's Compactness Theorem for Ricci flow Peter Topping 1 Applications of Hamilton's Compactness Theorem for Ricci flow 3 Overview 3 Background reading 4 Lecture 1. Ricci flow basics – existence and singularities 5 1.1. Initial PDE remarks 5 1.2. Basic Ricci flow theory 6 Lecture 2. Cheeger-Gromov convergence and Hamilton's compactness theorem 9 2.1. Convergence a...

In the present paper we have studied an N(k)-quasi Einstein manifold satisfying R(ξ, X).P̃ , where P̃ is the pseudo-projective curvature tensor. Among others, it is shown that if quasi-Einstein manifold with constant associated scalars is Ricci symmetric then the generator of the manifold is a Killing vector field. AMS Mathematics Subject Classification (2000): 53C25

Three propositions about Jordan matrices are proved and applied to algebraically classify the Ricci tensor in n-dimensional Kaluza-Klein-type spacetimes. We show that the possible Segre types are [1, 1 . . . 1], [21 . . . 1], [31 . . . 1], [zz̄1 . . . 1] and degeneracies thereof. A set of canonical forms for the Segre types is obtained in terms of semi-null bases of vectors.

In the study of conformai geometry, the method of elliptic partial differential equations is playing an increasingly significant role. Since the solution of the Yamabe problem, a family of conformally covariant operators (for definition, see section 2) generalizing the conformai Laplacian, and their associated conformai invariants have been introduced. The conformally covariant powers of the La...

In the study of conformal geometry, the method of elliptic partial differential equations is playing an increasingly significant role. Since the solution of the Yamabe problem, a family of conformally covariant operators (for definition, see section 2) generalizing the conformal Laplacian, and their associated conformal invariants have been introduced. The conformally covariant powers of the La...

One of the most interesting questions in Riemannian geometry is that of deciding whether a manifold admits curvatures of certain kinds. More specifically, one might want to know whether some given manifold admits a canonical metric, i.e. one with constant curvature of some form (sectional curvature, scalar curvature, etc.). (This will in fact have many topological implications.). One such probl...