Related papers: On a normalization of a Grassmann manifold

We show that every paracomplex space form is locally isometric to a modified Riemannian extension and give necessary and sufficient conditions so that a modified Riemannian extension is Einstein. We exhibit Riemannian extension Osserman…

The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in machine learning, computer vision and image processing to low-rank matrix optimization problems,…

The decomposition of the spinor bundle of the spin Grassmann manifolds $G_{m,n}=SO(m+n)/SO(m)\times SO(n)$ into irreducible representations of $\mathfrak{so}(m)\oplus\mathfrak{so}(n)$ is presented. A universal construction is developed and…

The existence of a recurrent spinor field on a pseudo-Riemannian spin manifold $(M,g)$ is closely related to the existence of a parallel 1-dimensional complex subbundle of the spinor bundle of $(M,g)$. We characterize the following simply…

We describe all affine maps from a Riemannian manifold to a metric space and all possible image spaces.

A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions,…

We generalize the concept of Fermi normal coordinates adapted to a geodesic to the case where the tangent space to the manifold at the base point is decomposed into a direct product of an arbitrary number of subspaces, so that we follow…

Explicit description for arbitrary Newtonian dynamical system admitting the normal shift in Riemannian manifold of the dimension $n\geq 3$ is found. On the base of this result the kinematics of normal shift of hypersurfaces along…

The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a natural symmetry condition on the shift-invariant subspaces that corresponds to considering an…

We study some sub-Riemannian objects (such as horizontal connectivity, horizontal connection, horizontal tangent plane, horizontal mean curvature) in hypersurfaces of sub-Riemannian manifolds. We prove that if a connected hypersurface in a…

It is well known that one can parameterize 2-D Riemannian structures by conformal transformations and diffeomorphisms of fiducial constant curvature geometries; and that this construction has a natural setting in general relativity theory…

The notion of a parallelizable distribution has been introduced and investigated. A non-integrable parallelizable distribution carries a natural sub-Riemannian structure. The geometry of this structure has been studied from the bi-viewpoint…

In a Riemannian manifold, the existence of a new connection is proved. In particular cases, this connection reduces to several symmetric, semi-symmetric and quarter-symmetric connections; even some of them are not introduced so far. We also…

Almost paracontact almost paracomplex Riemannian manifolds of the lowest dimension are studied. Such structures are constructed on hyperspheres in 4-dimensional spaces, Euclidean and pseudo-Euclidean, respectively. The obtained manifolds…

Almost paracontact Riemannian manifolds of the lowest dimension are studied, whose paracontact distributions are equipped with an almost paracomplex structure. These manifolds are constructed as a product of a real line and a 2-dimensional…

This paper contains a thorough introduction to the basic geometric properties of the manifold of Lagrangian subspaces of a linear symplectic space, known as the Lagrangian Grassmannian. It also reviews the important relationship between…

An almost-Riemannian structure on a surface is a generalized Riemannian structure whose local orthonormal frames are given by Lie bracket generating pairs of vector fields that can become collinear. The distribution generated locally by…

A compactification over $\overline{M}_g$ of $M_{g,n}$ is obtained by considering the relative Fulton-MacPherson configuration space of the universal curve. The resulting compactification differs from the Deligne-Mumford space…

[1] investigates advanced connotations of Hardy and Rellich-type inequalities on complete noncompact Riemannian manifolds, delving on deriving inequalities that incorporate poignant weight functions. These inequalities prolongate classical…

We generalize here our general procedure for constructing constant curvature maps of 2-spheres into Grassmannian manifolds G(m,n) this time concentrating our attention on maps which are non-holomorphic. We present some expressions…