In this paper, we study lightlike submanifolds of indefinite Kaehler manifolds. We introduce a class of lightlike submanifold called semi-invariant lightlike submanifold. We consider lightlike submanifold with respect to a quarter-symmetric non metric connection which is determined by the complex structure. We give some equivalent conditions for integrability of distributions with respect to th...

We study submanifolds of a Riemannian manifold with a semi-symmetric non-metric connection. We prove that the induced connection is also a semi-symmetric non-metric connection. We consider the total geodesicness, total umbilicity and the minimality of a submanifold of a Riemannian manifold with the semi-symmetric non-metric connection. We have obtained the Gauss, Codazzi and Ricci equations wit...

We obtain curvature tensor R̃(X, Y )Z w.r.t quarter-symmetric metric connection in terms of curvature tensor R(X,Y )Z relative to the Levi-civita connection in a K-contact manifold. Further, locally φ-symmetric, φ-symmetric and locally projective φ-symmetric K-contact manifolds with respect to the quarter-symmetric metric connection are studied and some results are obtained. The results are assi...

Let M be a differentiable manifold. We say that a tensor field g defined on M is non-regular if g is in some local L space or if g is continuous. In this work we define a mollifier smoothing gε of g that has the following feature: If g is a Riemannian metric of class C, then the Levi-Civita connection and the Riemannian curvature tensor of gε converges to the Levi-Civita connection and to the R...

We start from the pure Einstein-Hilbert action S = λ 2 R ⋆ 1 in Metric-Affine-Gravity, with the orthonormal metric g ab = η ab. We get an effective Levi-Civita Dilaton gravity theory in which the Dilaton field is related to the scaling of the gravitational coupling. When the Weyl symmetry is broken the resulting Einstein-Hilbert term is equivalent to the Levi-Civita one, using the projective in...

In this paper we introduce the Cheeger-Gromoll type metric on coframe bundle of a Riemannian manifold and investigate Levi-Civita connection, curvature tensor, sectional geodesics with metric.

In this paper, we present the classification of 2 and 3-dimensional Calabi hypersurfaces with parallel Fubini-Pick form respect to Levi-Civita connection metric.

Symmetric connections that are compatible with semi-Riemannian metrics can be characterized using an existence result for an integral leaf of a (possibly non integrable) distribution. In this paper we give necessary and sufficient conditions for a left-invariant connection on a Lie group to be the Levi–Civita connection of some semi-Riemannian metric on the group. As a special case, we will con...

We analyze the Dirac Laplacian of a one-parameter family of Dirac operators on a compact Lie group, which includes the Levi-Civita, cubic, and trivial Dirac operators. More specifically, we describe the Dirac Laplacian action on any Clifford module in terms of the action of the Lie algebra’s Casimir element on finitedimensional irreducible representations of the Lie group. Using this descriptio...

This is an in-progress set of notes describing the often-neglected geometrical, dynamical interpretation of a connection on a manifold. The essential idea is that, while the Levi-Civita connection is associated to the sliding action of parallel transport, it is perhaps more natural to think of a tangent space to a surface being rolled around as we move from point to point. The difference manife...