In this paper, we study half-lightlike submanifolds of a semi-Riemannian manifold such that the shape operator of screen distribution is conformal to the shape operator of screen transversal distribution. We mainly obtain some results concerning the induced Ricci curvature tensor and the null sectional curvature of screen transversal conformal half-lightlike submanifolds. 2010 Mathematics Subje...

Let $(M^{m}, g)$ be a Riemannian manifold and $TM$ its tangent bundle equipped with deformed Sasaki metric. In this paper, firstly we investigate all forms of curvature tensors (Riemannian tensor, Ricci curvature, sectional scalar curvature). Secondly, study the geometry unit metric, where presented formulas Levi-Civita connection also

This paper presents a rank rigidity result for negatively curved spaces. Let M be a compact manifold with negative sectional curvature and suppose that along every geodesic in M there is a parallel vector field making curvature −a with the geodesic direction. We prove that M has constant curvature equal to −a if M is odd dimensional, or if M is even dimensional and has sectional curvature pinch...

Given a finite dimensional manifold N , the group DiffS(N) of diffeomorphism of N which fall suitably rapidly to the identity, acts on the manifold B(M,N) of submanifolds on N of diffeomorphism type M where M is a compact manifold with dimM < dimN . For a right invariant weak Riemannian metric on DiffS(N) induced by a quite general operator L : XS(N)→ Γ(T ∗N⊗vol(N)), we consider the induced wea...

We prove Cheng’s eigenvalue comparison theorems [4] for geodesic balls within the cut locus under weaker geometric hypothesis, Theorems (1.1, 3.1, 3.2) and we also show that there are certain geometric rigidity in case of equality of the eigenvalues. This rigidity becomes isometric rigidity under upper sectional curvature bounds or lower Ricci curvature bounds. We construct examples of smooth m...

Every surface in the three dimensional Euclidean space have a canonical Riemannian metric, which induces constant Gaussian curvature and is conformal to the original metric. Discrete curvature flow is a feasible way to compute such canonical metrics. Similarly, three dimensional manifolds also admit canonical metrics, which induce constant sectional curvature. Canonical metrics on 3manifolds ar...

OBJECTIVE Quantification of the maximum anatomical cross-sectional area of the lumbar back muscles as a function of torso flexion angle and development of prediction equations as a function of torso flexion and anthropometric measures. BACKGROUND Cross-sectional areas of the lumbar back muscles used as inputs into biomechanical models have traditionally been derived from subjects lying in the...

in this paper, the time-like hyperruled surfaces in the minkowski 4-space and their algebraicinvariants are worked. also some characteristic results are found about these algebraic invariants.