In this note a proof is given for local existence and uniqueness of minimal surfaces with the topology of the halfplane respectively a cylinder of Lorentzian type with values in certain Lorentzian manifolds for given initial values up to the first derivatives. Global existence is proved for the case that the target manifold is diffeomorphic to Rn.

We prove an extension of the Index Theorem for Morse–Sturm systems of the form −V ′′ + RV = 0, where R is symmetric with respect to a (non positive) symmetric bilinear form, and thus the corresponding differential operator is not self-adjoint. The result is then applied to the case of a Jacobi equation along a geodesic in a Lorentzian manifold, obtaining an extension of the Morse Index Theorem ...

A pp-wave is a Lorentzian manifold with a parallel light-like vector field satisfying a certain curvature condition. We introduce generalisations of pp-waves, on one hand by allowing the vector field to be recurrent and on the other hand by weakening the curvature condition. These generalisations are related to the screen holonomy of the Lorentzian manifold. While pp-waves have a trivial screen...

We consider the simplicial state-sum model of Ponzano and Regge as a path integral for quantum gravity in three dimensions. We examine the Lorentzian geometry of a single 3-simplex and of a simplicial manifold, and interpret an asymptotic formula for 6j-symbols in terms of this geometry. This extends Ponzano and Regge’s similar interpretation for Euclidean geometry. We give a geometric interpre...

휂-Ricci solitons on Lorentzian 훽-Kenmotsu manifold are considered an manifolds satisfying certain curvature Conditions, R(ξ,X).S=0, S(ξ,X).R=0, W2(ξ,X).S=0,S(ξ,X).W2=0 We proved that in β-Kenmotsu (M,φ,ξ,η,푔). Then the existence of implies M is Einstein and if Ricci tensor satisfies, then steady. If condition 휇=0, 휆=0, which shows 휆is steady

We define a physically reasonable mass for an asymptotically Robertson-Walker (ARW) manifold which is uniquely defined in the case of a normalized representation.

The present study initially introduced a new type Lorentzian almost para contact manifold using the generalized symmetric metric connections of $(\alpha,\beta)$. Later, some results is given about manifold.
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