On Growth and Form and Geometry. I
On H. Weyl and H. Minkowski polynomials.
On Hamiltonian submanifolds.
On Hamiltonian-minimal Lagrangian tori in .
On harmonic vector fields.
A tangent bundle to a Riemannian manifold carries various metrics induced by a Riemannian tensor. We consider harmonic vector fields with respect to some of these metrics. We give a simple proof that a vector field on a compact manifold is harmonic with respect to the Sasaki metric on TM if and only if it is parallel. We also consider the metrics II and I + II on a tangent bundle (cf. [YI]) and harmonic vector fields generated by them.
On Harnack's inequalities for the Kähler-Ricci flow.
On Hb-flat Hyperbolic Kaehlerian Spaces
On Helices in the Euclidean n-Space.
On Hermitian manifold with torsion.
Analytic vector fields in a Hermitian manifold have been studied by various authors [3, 4, 6 & 7]. Boothby [2] and Goldberg [1] extended some of these results to Hermitian manifold with torsion. In this paper we define and study p-pseudo-analytic vector fields, which when p = 1, reduce to analytic vector fields as given in [1] and [2]. A necessary and sufficient condition for a vector field to be covariant (contravariant) p-pseudo-analytic has been obtained and their relationship with p-pseudo-harmonic...
On hierarchy of the positioned eco-grammar systems
Positioned eco-grammar systems (PEG systems, for short) were introduced in our previous papers. In this paper we engage in a new field of research, the hierarchy of PEG systems, namely in the hierarchy of the PEG systems according to the number of agents presented in the environment and according to the number of types of agents in the system.
On higher order geometry on anchored vector bundles
Some geometric objects of higher order concerning extensions, semi-sprays, connections and Lagrange metrics are constructed using an anchored vector bundle.
On higher order point singularities of some geometric object fields
On Holomorphic and Anti-Holomorphic Sectional Curvature of Indefinite Kähler Manifolds of Real Dimension n... 6.
On holomorphically projective mappings from equiaffine generally recurrent spaces onto Kählerian spaces
In this paper we consider holomorphically projective mappings from the special generally recurrent equiaffine spaces onto (pseudo-) Kählerian spaces . We proved that these spaces do not admit nontrivial holomorphically projective mappings onto . These results are a generalization of results by T. Sakaguchi, J. Mikeš and V. V. Domashev, which were done for holomorphically projective mappings of symmetric, recurrent and semisymmetric Kählerian spaces.
On holomorphically projective mappings from equiaffine symmetric and recurrent spaces onto Kählerian spaces
On holomorphically projective mappings from manifolds with equiaffine connection onto Kähler manifolds
In this paper we study fundamental equations of holomorphically projective mappings from manifolds with equiaffine connection onto (pseudo-) Kähler manifolds with respect to the smoothness class of connection and metrics. We show that holomorphically projective mappings preserve the smoothness class of connections and metrics.
On holomorphically projective mappings of -Kähler manifolds
In this paper we study fundamental equations of holomorphically projective mappings of -Kähler spaces (i.e. classical, pseudo- and hyperbolic Kähler spaces) with respect to the smoothness class of metrics. We show that holomorphically projective mappings preserve the smoothness class of metrics.
On holomorphically projective mappings onto Kählerian spaces
The main result of this paper determines a system of linear partial differential equations of Cauchy type whose solutions correspond exactly to holomorphically projective mappings of a given equiaffine space onto a Kählerian space. The special case of constant holomorphic curvature is also studied.
On holonomicity criteria in second order geometry.
On homogeneous conformally symmetric pseudo-Riemannian manifolds