The object of this paper is to study invariant submanifoldsM of Sasakian manifolds ̃ M admitting a semisymmetric nonmetric connection, and it is shown that M admits semisymmetric nonmetric connection. Further it is proved that the second fundamental forms σ and σ with respect to Levi-Civita connection and semi-symmetric nonmetric connection coincide. It is shown that if the second fundamental fo...

A local uniqueness property of holomorphic functions on realanalytic nowhere minimal CR submanifolds of higher codimension is investigated. A sufficient condition called almost minimality is given and studied. A weaker necessary condition, being contained a possibly singular real-analytic Levi-flat hypersurface is studied and characterized. This question is completely resolved for algebraic sub...

We obtain the most general static cylindrically symmetric vacuum solutions of the Einstein field equations in (4+N) dimensions. Under the assumption of separation of variables, we construct a family of Levi-Civita-Kasner vacuum solutions in (4 + N). We discuss the dimensional reduction of the static solutions. Depending on the reduction procedure, they can be interpreted either as a scalar-vacu...

Belief revision is the process of revising beliefs in light of new information. Belief contraction is the process of giving up beliefs to make them consistent with new information. The Levi and Harper Identities provide constructions of revisions and contractions in terms of each other. This paper gives necessary and sufficient conditions for when revisions can be constructed from contractions,...

As is well known, a metric on a manifold determines a unique symmetric connection for which the metric is parallel: the Levi-Civita connection. In this paper we investigate the inverse problem: to what extent is the metric of a Riemannian manifold determined by its LeviCivita connection? It is shown that for a generic Levi-Civita connection of a metric h there exists a set of positive semi-defi...

Kátia Luz Torres, Adriana Malheiro, Adriana Tateno, Tatiane Amabile de Lima, Laura Patricia Viana Maia, João Paulo Diniz Pimentel, Márcia Poinho Encarnação de Morais, Christiane Santana de Melo Usui, Flavia de Oliveira Braga, Igor Araújo Ferreira Silva, Felicien Vasquez, and José Eduardo Levi Author affi liations: Fundação de Hematologia e Hemoterapia do Amazonas, Manaus, Amazon, Brazil (K.L. T...

Abstract Holomorphically homogeneous Cauchy–Riemann (CR) real hypersurfaces $M^3 \subset \mathbb{C}^2$ were classified by Élie Cartan in 1932. In the next dimension, we complete classification of simply-transitive Levi non-degenerate $M^5 \mathbb{C}^3$ using a novel Lie algebraic approach independent any earlier classifications abstract algebras. Central to our is new coordinate-free formula fo...

We discuss local polynomial convexity of real analytic Levi-flat hypersurfaces in [Formula: see text], near singular points.