Related papers: Pseudo-Riemannian metrics with parallel spinor fie…

The main object of the present paper is to study the geometric properties of a generalized Roter type semi-Riemannian manifold, which arose in the way of generalization to find the form of the Riemann-Christoffel curvature tensor $R$. Again…

It is shown that the horizontal holonomy group of a K-contact sub-Riemannian manifold either coincides with the holonomy group of a Riemannian manifold, or it is a codimension-one normal subgroup of the later group. The question of…

In the present article the geometry of semi-Riemannian manifolds with nonholonomic constraints is studied. These manifolds can be considered as analogues to the sub-Riemannian manifolds, where the positively definite metric is substituted…

Every Heisenberg manifold has a natural "sub-Riemannian" metric with interesting properties. We describe the corresponding noncommutative metric structure for Rieffel's quantum Heisenberg manifolds.

In this text we combine the notions of supergeometry and supersymmetry. We construct a special class of supermanifolds whose reduced manifolds are (pseudo) Riemannian manifolds. These supermanifolds allow us to treat vector fields on the…

We describe a new realization of supersymmetry, called scalar supersymmetry, acting in spaces of differential forms (bi-spinors), where transformation parameters are Lorentz scalars instead of spinors. The realization is related but is not…

Para-Ricci-like solitons with arbitrary potential on para-Sasaki-like Riemannian $\Pi$-manifolds are introduced and studied. For the studied soliton, it is proved that its Ricci tensor is a constant multiple of the vertical component of…

Object of study are para-Ricci-like solitons on para-Sasaki-like almost paracontact almost paracomplex Riemannian manifolds, briefly, Riemannian $\Pi$-manifolds. Different cases when the potential of the soliton is the Reeb vector field or…

This short note concerns with two inequalities in the geometry of gradient Ricci solitons $(g, f, \lambda )$ on a smooth manifold $M$. These inequalities provide some relationships between the curvature of the Riemannian metric $g$ and the…

Ricci-like solitons on Sasaki-like almost contact B-metric manifolds are the object of study. Cases, where the potential of the Ricci-like soliton is the Reeb vector field or pointwise collinear to it, are considered. In the former case,…

In this paper, we show several vanishing type theorems for $p$-harmonic $\ell$-forms on Riemannian manifolds ($p\geq2$). First of all, we consider complete non-compact immersed submanifolds $M^n$ of ${N}^{n+m}$ with flat normal bundle, we…

Let $f:N\rightarrow (M,g)$ be an oriented (or spin), complete, stable, minimal, immersed hypersurface. In this paper we establish various vanishing theorems for the space of $L^2$-harmonic forms and spinors (in the spin case) under suitable…

The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds of arbitrary index, using one-sided bounds on the Riemann tensor which in the Riemannian…

In this paper we extend the Cartan's approach of Riemannian normal coordinates and show that all n-dimensional pseudo-Riemannian metrics are conformal to a flat manifold, when, in normal coordinates, they are well-behaved in the origin and…

We show that the pseudo-Riemannian geometry of submanifolds can be formulated in terms of higher order multi-linear maps. In particular, we obtain a Poisson bracket formulation of almost (para-)K\"ahler geometry.

The torsion of every metric connection on a Riemannian manifold has three components: one totally skew-symmetric, one of vectorial type, and one of twistorial type. In this paper we classify complete simply connected Riemannian manifolds…

This text is an introductory review of the basic concepts of the theory of semi-Riemannian geometry on real finite-dimensional manifolds without boundary.

Two pseudo-Riemannian metrics $g $ and $\bar g$ are geodesically equivalent, if they share the same (unparameterized) geodesics. We give a complete local description of such metrics which solves the natural generalisation of Beltrami…

For a complete Riemannian manifold $M$ with an (1,1)-elliptic Codazzi self-adjoint tensor field $A$ on it, we use the divergence type operator ${L_A}(u): = div(A\nabla u)$ and an extension of the Ricci tensor to extend some major comparison…

A four-dimensional Walker geometry is a four-dimensional manifold M with a neutral metric g and a parallel distribution of totally null two-planes. This distribution has a natural characterization as a projective spinor field subject to a…