Let Mn be a Riemannian n-manifold. Denote by S(p) and Ric(p) the Ricci tensor and the maximum Ricci curvature on Mn, respectively. In this paper we prove that every C-totally real submanifolds of a Sasakian space form M̄2m+1(c) satisfies S ≤ ( (n−1)(c+3) 4 + n 2 4 H2)g, where H2 and g are the square mean curvature function and metric tensor on Mn, respectively. The equality holds identically if ...

I identify the class of even-dimensional conformal field theories that is most similar to two-dimensional conformal field theory. In this class the formula, elaborated recently, for the irreversibility of the renormalization-group flow applies also to massive flows. This implies a prediction for the ratio between the coefficient of the Euler density in the trace anomaly (charge a) and the stres...

In recent papers [1-3], we have discussed matter symmetries of non-static spherically symmetric spacetimes, static plane symmetric spacetimes and cylindrically symmetric static spacetimes. These have been classified for both cases when the energy-momentum tensor is non-degenerate and also when it is degenerate. Here we add up some consequences and the missing references about the Ricci tensor. ...

We consider alternative theories of gravity with a direct coupling between matter and the Ricci scalar We study the relation between these theories and ordinary scalar-tensor gravity, or scalar-tensor theories which include nonstandard couplings between the scalar and matter. We then analyze the motion of matter in such theories, its implications for the Equivalence Principle, and the recent cl...

A new approach to the algebraic classification of second order symmetric tensors in 5-dimensional space-times is presented. The possible Segre types for a symmetric two-tensor are found. A set of canonical forms for each Segre type is obtained. A theorem which collects together some basic results on the algebraic structure of the Ricci tensor in 5-dimensional space-times is also stated. ∗ inter...

1. The main result and some consequences. In 1956 E. Calabi [6] attacked the classification problem of compact euclidean space forms by means of a special construction, called the Calabi construction (see Wolf [14, p. 124]). Here we announce that the construction can be extended to compact riemannian manifolds whose Ricci curvature tensor is zero (Ricci flat). Of course, it is not known if ther...

We prove that any gradient shrinking Ricci soliton has at most Euclidean volume growth. This improves a recent result of H.-D. Cao and D. Zhou by removing a condition on the growth of scalar curvature. A complete Riemannian manifold M of dimension n is called gradient shrinking Ricci soliton if there exists f ∈ C (M) and a constant ρ > 0 such that Rij +∇i∇jf = ρgij , where Rij denotes the Ricci...

Ghost neutrino solution in radiative Kerr spacetime endowed with totally skew-symmetric Cartan contortion is presented. The computations are made by using the Newman-Penrose (NP) calculus. The model discussed here maybe useful in several astrophysical applications specially in black hole astrophysics. PACS number(s): 0420, 0450 Departamento de F́ısica Teorica-UERJ. Rua São Fco. Xavier 524, Rio d...

We study basic properties of supermanifolds endowed with an even (odd) symplectic structure and a connection respecting this symplectic structure. Such supermanifolds can be considered as generalization of Fedosov manifolds to the supersymmetric case. Choosing an appropriate definition of inverse (second-rank) tensor fields on supermanifolds we consider the symmetry behavior of tensor fields as...