Let (M, g) be an oriented 4-dimensional Riemannian manifold (not necessarily compact). Due to the Hodge-star operator ⋆, we have a decomposition of the bivector bundle ∧2 TM = ∧+ ⊕ ∧− . Here ∧± is the eigen-subbundle for the eigenvalue ±1 of ⋆. The metric g on M induces a metric, denoted by < , >, on the bundle ∧2 TM . Let π : Z = S (∧+) −→ M be the sphere bundle; the fiber over a point m ∈ M p...

pseudo ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo ricci symmetric real hypersurfaces of the complex projective space cpn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.

1. Invariants. A contact sub-Riemannian metric is a triple (X,∆, g) consisting of a (2n+ 1)-dimensional manifold X, a distribution ∆ on X, which is a contact structure, and a metric g on ∆. It defines a metric on X by measuring via g the length of smooth curves that are tangent to ∆. All the considerations in this paper are local: we consider only germs (X,∆, g)q0 at a fixed point q0. There are...

Let X be a G-space such that the orbit space X/G is metrizable. Suppose a family of slices is given at each point of X. We study a construction which associates, under some conditions on the family of slices, with any metric on X/G an invariant metric on X. We show also that a family of slices with the required properties exists for any action of a countable group on a locally compact and local...

The asymptotic expansion of the volume of an asymptotically hyperbolic Einstein (AHE) metric defines invariants of the AHE metric and of a metric in the induced conformal class at infinity. These have been of recent interest, motivated in part by the AdS/CFT correspondence in physics. In this paper we derive some new properties of these invariants. Let (X, g+) be AHE with smooth conformal infin...

Correspondence: [email protected]. edu.tw Department of Applied Mathematics, National Hsinchu University of Education, No. 521 Nanda Rd., Hsinchu City 300, Taiwan Abstract In this article, for a tυs-G-cone metric space (X, G) and for the family A of subsets of X, we introduce a new notion of the tυs H cone metric H with respect to G, and we get a fixed result for the stronger Meir-Keeler-G-cone-t...