The decomposition of global conformal invariants: some technical proofs. I.
The geometric structure of the inverse gamma distribution.
The geometric structure of the Pareto distribution.
The Group of Invertible Elements of the Algebra of Quaternions
We have, that all two-dimensional subspaces of the algebra of quaternions, containing a unit, are 2-dimensional subalgebras isomorphic to the algebra of complex numbers. It was proved in the papers of N. E. Belova. In the present article we consider a 2-dimensional subalgebra of complex numbers with basis and we construct the principal locally trivial bundle which is isomorphic to the Hopf fibration.
The Jordan normal form of higher order Osserman algebraic curvature tensors
We construct new examples of algebraic curvature tensors so that the Jordan normal form of the higher order Jacobi operator is constant on the Grassmannian of subspaces of type in a vector space of signature . We then use these examples to establish some results concerning higher order Osserman and higher order Jordan Osserman algebraic curvature tensors.
The nonexistence of rank 4 IP tensors in signature .
The Projectivization of Conformal Models of Fibrations Determined by the Algebra of Quaternions
Our aim is to study the principal bundles determined by the algebra of quaternions in the projective model. The projectivization of the conformal model of the Hopf fibration is considered as example.
The reconstruction theorem
The spectral geometry of the Weyl conformal tensor
We study when the Jacobi operator associated to the Weyl conformal curvature tensor has constant eigenvalues on the bundle of unit spacelike or timelike tangent vectors. This leads to questions in the conformal geometry of pseudo-Riemannian manifolds which generalize the Osserman conjecture to this setting. We also study similar questions related to the skew-symmetric curvature operator defined by the Weyl conformal curvature tensor.
The spread of the shape operator as conformal invariant.
The volume of geodesic disks in a Riemannian manifold
The volumes of small geodesic balls for a metric connection
Theorems concerning certain special tensor fields on Riemannian manifolds and their applications.
Theory of semisymmetric conformally flat and biharmonic submanifolds.
TheStructure of Nearly Kähler Manifolds.
Torsion Free Connections, Topology, Geometry and Differential Operators on Smooth Manifolds
Totally umbilical submanifolds in some semi-Riemannian manifolds
We investigate totally umbilical submanifolds in manifolds satisfying some curvature conditions of either recurrent or pseudosymmetry type in the sense of Ryszard Deszcz and derive the respective condition for submanifolds. We also prove some relations involving the mean curvature and the Weyl conformal curvature tensor of submanifolds. Some examples are discussed.
Trace decomposition and recurrency
Trigonometrische Charakterisierung der Räume konstanter Krümmung.