相关论文: Harmonic Riemannian submersions between Riemannian…

The index of a Riemannian symmetric space is the minimal codimension of a proper totally geodesic submanifold (Onishchik, 1980). There is a conjecture by the first two authors for how to calculate the index. In this paper we give an…

Minimal submanifolds constitute a central area within the realm of differential geometry, due to their many applications in various branches of physics. In this thesis we will employ a recent result of S. Gudmundsson and T.J. Munn to…

This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the K\"ahler class, is used to define and characterize a special class…

In this paper, we define and study strong right-invariant sub-Riemannian structures on the group of diffeomorphisms of a manifold with bounded geometry. We derive the Hamiltonian geodesic equations for such structures, and we provide…

We classify totally geodesic and parallel hypersurfaces of four-dimensional non-reductive homogeneous pseudo-Riemannian manifolds.

In the present paper we show that the geodesic flows of a sub-Riemannian metric and that of a Riemannian extension commute if and only if the extended metric is parallel with respect to a certain connection. This helps us to describe the…

In this survey article we provide an introduction to submanifold geometry in symmetric spaces of noncompact type. We focus on the construction of examples and the classification problems of homogeneous and isoparametric hypersurfaces, polar…

We consider isometric immersions of complete connected Riemannian manifolds into space forms of nonzero constant curvature. We prove that if such an immersion is compact and has semi-definite second fundamental form, then it is an embedding…

We show geodesic completeness of certain compact locally symmetric pseudo-Riemannian manifolds of signature $(2,n)$. Our model space $\mathbf{X}$ is a $1$-connected, indecomposable symmetric space of signature $(2,n)$, that admits a unique…

In this paper we give a unified framework for the construction of complex valued harmonic morphisms from the real, complex and quaternionic Grassmannians and their non-compact duals. This gives a positive answer to the corresponding open…

The notion of hidden symmetry algebra used in the context of exactly solvable systems is re-examined from the purely algebraic way, analyzing subspaces of commuting polynomials that generate finite-dimensional quadratic algebras. By…

In this paper, we establish a sufficient condition for a geodesic in a Riemannian manifold to be homogeneous, i.e. an orbit of an $1$-parameter isometry group. As an application of this result, we provide a new proof of the fact that every…

A foliation on a Riemannian manifold is hyperpolar if it admits a flat section, that is, a connected closed flat submanifold that intersects each leaf of the foliation orthogonally. In this article we classify the hyperpolar homogeneous…

In this paper we are concerned with harmonic maps and minimal immersions defined on compact Riemannian manifolds and with values in homogenous strongly harmonic manifolds. We show some results on the Morse index by varying these maps along…

In this paper, we give a necessarly and sufficient condition for orbits of linear isotropy representations of Riemannian symmetric spaces are biharmonic submanifolds in hyperspheres in Euclidean spaces. In particular, we obtain examples of…

We consider 5-dimensional Lie groups with left-invariant Riemannian metrics. For such groups we give a partial classification of left-invariant conformal foliations with minimal leaves of codimension 2. These foliations produce local…

We study isometric actions on Riemannian symmetric spaces of noncompact type which are induced by reductive algebraic subgroups of the isometry group. We show that for such an action there exists a corresponding isometric action on a dual…

We show the existence of isometric (or Ford) fundamental regions for a large class of subgroups of the isometry group of any rank one Riemannian symmetric space of noncompact type. The proof does not use the classification of symmetric…

Riemannian geodesic orbit spaces (G/H,g) are natural generalizations of symmetric spaces, defined by the property that their geodesics are orbits of one-parameter subgroups of G. We study the geodesic orbit spaces of the form (G/S,g), where…

We prove that any base space of Riemannian submersion from a compact Lie group (with bi-invariant metric) must have a basic property previously known for normal biquotients; namely, any zero-curvature plane exponentiates to a flat.