Sub-Riemannian Geometry is proved to play an important role in many applications, e.g., Mathematical Physics and Control Theory. Sub-Riemannian Geometry enjoys major differences from the Riemannian being a generalization of the latter at the same time, e.g., geodesics are not unique and may be singular, the Hausdorff dimension is larger than the manifold topological dimension. There exists a la...

An isometric immersion f : Mn → M̃n from a Riemannian nmanifold Mn into a Kähler n-manifold M̃n is called Lagrangian if the complex structure J of the ambient manifold M̃n interchanges each tangent space of Mn with the corresponding normal space. In this paper, we completely classify spherical Lagrangian submanifolds in complex Euclidean spaces. In this paper, we also provide two corresponding cla...

Considering pseudo-Riemannian $g$-natural metrics on tangent bundles, we prove that the condition of being Ricci soliton is hereditary in sense a structure bundle gives rise to base manifold. Restricting ourselves some class metrics, show if and only manifold flat potential vector field complete lift conformal field. We give then classification fields Riemannian When unit bundles over constant ...

In this paper, we introduce the notion of a semi-slant pseudoRiemannian submersion from an indefinite almost contact 3-structure manifold onto a pseudo-Riemannian manifold. We investigate the geometry of foliations determined by horizontal and vertical distributions and provide a non-trivial example. We also find a necessary and sufficient condition for a semi-slant submersion to be totally geo...

The present article serves the purpose of pursuing Geometrization of heat flow on volumetrically isothermal manifold by means of RF approach. In this article, we have analyzed the evolution of heat equation in a 3-dimensional smooth isothermal manifold bearing characteristics of Riemannian manifold and fundamental properties of thermodynamic systems. By making use of the notions of various curva...

In this article we study conditions for the integrability of the distribution defined on a regular Poisson manifold as the orthogonal complement (with respect to a pseudo-Riemannian metric) to the tangent spaces of the leaves of a symplectic foliation. Examples of integrability and non-integrability of this distribution are provided.

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.

We classify the five dimensional C Anosov flows which have C-Anosov splitting and preserve a smooth pseudo-Riemannian metric . Up to a special time change and finite covers, such a flow is C flow equivalent either to the suspension of a symplectic hyperbolic automorphism of T4, or to the geodesic flow on a three dimensional hyperbolic manifold.