In this paper, we investigate semi-invariant Riemannian submersion from a Kaehler manifold with semi-symmetric non-metric connection to manifold. We study the geometry of foliations connection. Later, introduce base be local product

It is shown that the Hermitian-symmetric space CP1 × CP1 × CP1 and the flag manifold F1,2 endowed with any left invariant metric admit no compatible integrable almost complex structures (even locally) different from the invariant ones. As an application it is proved that any stable harmonic immersion from F1,2 equipped with an invariant metric into an irreducible Hermitian symmetric space of co...

This paper presents a new similarity measure to be used for general tasks including supervised learning, which is represented by the K-nearest neighbor classifier (KNN). The proposed similarity measure is invariant to large differences in some dimensions in the feature space. The proposed metric is proved mathematically to be a metric. To test its viability for different applications, the KNN u...

This article is a follow up of the previous article of the authors on the analytic surgery of { and {invariants. We investigate in detail the (Atiyah{Patodi{Singer){ {invariant for manifolds with boundary. First we generalize the cut{and{paste formula to arbitrary boundary conditions. A priori the {invariant is an invariant of the Riemannian structure and a representation of the fundamental gro...

Invariant manifolds of equations governing the dynamics of conservative nonholonomic systems are investigated. These manifolds are assumed to be uniquely projected onto configuration space. The invariance conditions are represented in the form of generalized Lamb’s equations. Conditions are found under which the solutions to these equations admit a hydrodynamical description typical of Hamilton...

Abstract: Motivated by problems related to quasi-local mass in general relativity, we study the static metric extension conjecture proposed by R. Bartnik [4]. We show that, for any metric on B̄1 that is close enough to the Euclidean metric and has reflection invariant boundary data, there always exists an asymptotically flat and scalar flat static metric extension in M = R \B1 such that it satis...

unlike the classical deformation analysis of the earth crust, which derives the planar and vertical strains separately, in this study, we have offered a method for 3-d deformation study based on intrinsic geometry of the manifolds on the topographic surface of the earth. in this way, our method would be based on the 2-d metric tensor of horizontal deformation and 2-d curvature tensor of vertica...

For homogeneous reductive spaces G/H with reductive complements decomposable into an orthogonal sum m = m1⊕m2⊕m3 of three Ad(H)invariant irreducible mutually inequivalent submodules we establish simple conditions under which an invariant metric f -structure (f, g) belongs to the classes G1f , NKf , and Kill f of generalized Hermitian geometry. The statements obtained are then illustrated with f...

Let ϕ t be a continuous flow on a metric space X and I be an isolated invariant set