Related papers: Full description of totally geodesic unit vector f…

In this paper, we prove that the harmonicity of a metric on a pseudo-Riemannian manifold is equivalent to the harmonicity of both its Sasaki (resp. horizontal and complete) lift metric on the tangent bundle and its Sasaki lift metric on the…

We give a general description of the construction of weighted spherically symmetric metrics on vector bundle manifolds, i.e. the total space of a vector bundle $E\rightarrow M$, over a Riemannian manifold $M$, when $E$ is endowed with a…

We study the geodesic motion planning problem for complete Riemannian manifolds and investigate their geodesic complexity, an integer-valued isometry invariant introduced by D. Recio-Mitter. Using methods from Riemannian geometry, we…

We give a description of all $G$-invariant Ricci-flat K\"ahler metrics on the canonical complexification of any compact Riemannian symmetric space $G/K$ of arbitrary rank, by using some special local $(1,0)$ vector fields on $T(G/K)$. As…

In this paper we consider some properties of the three-dimensional homogeneous SO(2)-isotropic Riemannian manifolds. In particular, we determine the geodesics, the totally geodesic surfaces, the totally umbilical surfaces and the geodesics…

In this Note we establish a relation between sections in globally generated holomorphic vector bundles on K\"ahler manifolds, isotropic with respect to a non-degenerate quadratic form, and totally geodesic foliations on Euclidean open…

Given a closed Riemannian manifold $(M^m,g)$ and a vector field $v$ on $M$, we form the Sasaki metric $g_S$ on $TM$, and restrict it to the image of the cross section map of $M$ into $TM$ defined by $v$, whose pull back to $M$ defines a new…

In this article, I classify the totally geodesic submanifolds in the complex 2-Grassmannians and in the quaternionic 2-Grassmannians. It turns out that for both of these spaces, the earlier classification of maximal totally geodesic…

This work investigates biharmonic and interpolating sesqui-harmonic vector fields on the tangent bundle of a para-K\"ahler--Norden manifold (M, varphi, g) endowed with the varphi-Sasaki metric. We derive the first variation of the bienergy…

In this paper we give a characterization of real hypersurfaces in noncompact complex two-plane Grassmannian $SU_{2,m}/S(U_2 U_m)$, $m \geq 2$ with Reeb vector field $\xi$ belonging to the maximal quaternionic subbundle $\mathcal Q$. Then it…

The isotropic almost complex structures induce a Riemannian metric $g_{\delta,\sigma}$ on TM, which are the generalized type of Sasakian metric. In this paper, the Levi-Civita connection of $g_{\delta,\sigma}$ is calculated and the…

Sasakian manifolds provide explicit formulae of some Jacobi operators which describe the biharmonic equation of curves in Riemannian manifolds. In this paper we characterize non-geodesic biharmonic curves in Sasakian manifolds which are…

In this paper we explore the geometric structures associated with curvature radii of curves with values on a Riemannian manifold $(M, g)$. We show the existence of sub-Riemannian manifolds naturally associated with the curvature radii and…

The present paper deals with the study of invariant submanifolds of generalized Sasakian-space-forms with respect to Levi-Civita connection as well as semi-symmetric metric connection. We provide some examples of such submanifolds and…

A geodesic orbit manifold is a complete Riemannian manifold all of whose geodesics are orbits of one-parameter groups of isometries. We give both a geometric and an algebraic characterization of geodesic orbit manifolds that are…

We study constructions of vector fields with properties which are characteristic to Reeb vector fields of contact forms. In particular, we prove that all closed oriented odd-dimensional manifold have geodesible vector fields.

In this paper we show that for an invariant $(\alpha,\beta)-$metric $F$ on a homogeneous Finsler manifold $\frac{G}{H}$, induced by an invariant Riemannian metric $\tilde{a}$ and an invariant vector field $\tilde{X}$, the vector…

In this paper we investigate possible extensions of the idea of geodesic completeness in complex manifolds, following two directions: metrics are somewhere allowed not to be of maximum rank, or to have 'poles' somewhere else. Geodesics are…

We present a numerical implementation of the geodesic ray transform and its inversion over functions and solenoidal vector fields on two-dimensional Riemannian manifolds. For each problem, inversion formulas previously derived in…

We give a complete local classification of all Riemannian 3-manifolds $(M,g)$ admitting a nonvanishing Killing vector field $T$. We then extend this classification to timelike Killing vector fields on Lorentzian 3-manifolds, which are…