In this paper, we study the effects of the spontaneous curvature on the static deformation of a vesicle membrane under the elastic bending energy, with prescribed bulk volume and surface area. Generalizing the phase field models developed in our previous works, we deduce a new energy formula involving the spontaneous curvature effects. Several axis-symmetric configurations are obtained through ...

This paper aims to study some semi-symmetric and curvature tensor conditions on α-Kenmotsu pseudo-metric manifolds. Some of semi-symmetric, locally symmetric, the Ricci are considered such Also, relationships between M-projective conformal tensor, concircularly conharmonic investigated. Finally, an example structure is given.

Provided certain basic rank requirements are met, we establish a converse of the classical fact that if A is symmetric, then RA is an algebraic curvature tensor. This allows us to establish a simultaneous diagonalization result in the event that three algebraic curvature tensors are linearly dependent. We use these results to establish necessary and sufficient conditions that a set of two or th...

Copyright q 2010 Zisheng Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We extend the classical Bishop-Gromov volume comparison from constant Ricci curvature lower bound to radially symmetric Ricci curvature lower bound...

The Paneitz operator is a fourth order differential operator which arises in conformal geometry and satisfies a certain covariance property. Associated to it is a fourth order curvature – the Qcurvature. We prove the existence of a continuum of conformal radially symmetric complete metrics in hyperbolic space Hn, n > 4, all having the same constant Q-curvature. Moreover, similar results can be ...

We construct a new class of plane-symmetric solutions possessing a curvature singularity which is null and weak, like the spacetime singularity at the Cauchy horizon of spinning (or charged) black holes. We then analyse the stability of this singularity using a rigorous non-perturbative method. We find that within the framework of (linearly-polarized) plane-symmetric spacetimes this type of nul...

A Riemannian manifold is called harmonic if its volume density function expressed in polar coordinates centered at any point of the manifold is radial. Flat and rank-one symmetric spaces are harmonic. The converse (the Lichnerowicz Conjecture) is true for manifolds of nonnegative scalar curvature and for some other classes of manifolds, but is not true in general: there exists a family of homog...

We derive the equations of Gauss and Weingarten for a non-degenerate hypersurface of a semi-Riemannian manifold admitting a semi-symmetric metric connection, and give some corollaries of these equations. In addition, we obtain the equations of Gauss curvature and Codazzi-Mainardi for this non-degenerate hypersurface and give a relation between the Ricci and the scalar curvatures of a semi-Riema...

Based on the analogy with non-minimal SU(2) symmetric Wu-Yang monopole with regular metric, the solution describing a non-minimal U(1) symmetric Dirac monopole is obtained. In order to take into account the curvature coupling of gravitational and electromagnetic fields, we reconstruct the effective metrics of two types: the so-called associated and optical metrics. The optical metrics display e...

Let E be a natural operator associated to the curvature tensor of a pseudo-Riemannian manifold. We study when the spectrum, or more generally the real Jordan normal form, of E is constant on the natural domain of definition. In particular, we examine the Jacobi operator, the higher order Jacobi operator, the Szabo operator, and the skew-symmetric curvature operator.