SOME NEW IDENTITIES FOR THE SECOND COVARIANT DERIVATIVE OF THE CURVATURE TENSOR

In this paper we study the second covariant derivative of Riemannian curvature tensor. Some new identities for the second covariant derivative are given. Namely, identities obtained by cyclic sum with respect to three indices are given. In the first case, two curvature tensor indices and one covariant derivative index participate in the cyclic sum, while in the second case one curvature tensor index and two covariant derivative indices participate in the cyclic sum

Equitorsion holomorphically projective mappings of generalized Kählerian space of the first kind

summary:In this paper we define generalized Kählerian spaces of the first kind $(G\underset 1K_N)$ given by (2.1)--(2.3). For them we consider hollomorphically projective mappings with invariant complex structure. Also, we consider equitorsion geodesic mapping between these two spaces ($G\underset 1K_N$ and $G\underset 1{\overline K}_N$) and for them we find invariant geometric objects

On Conformal and Concircular Diffeomorphisms of Eisenhart’s Generalized Riemannian Spaces

We consider conformal and concircular mappings of Eisenhart’s generalized Riemannian spaces. We prove conformal and concircular invariance of some tensors in Eisenhart’s generalized Riemannian spaces. We give new generalizations of symmetric spaces via Eisenhart’s generalized Riemannian spaces. Finally, we describe some properties of covariant derivatives of tensors analogous to Yano’s tensor of concircular curvature in Eisenhart symmetric spaces of various kinds

Generalized Riemann Spaces

summary:In this paper we investigate holomorphically projective mappings of generalized Kählerian spaces. In the case of equitorsion holomorphically projective mappings of generalized Kählerian spaces we obtain five invariant geometric objects for these mappings

SOME RELATIONS IN THE GENERALIZED KÄHLERIAN SPACES OF THE SECOND KIND

Starting from the definition of generalized Riemannian space (GRN) [1], in which a non-symmetric basic tensor gij is introduced, in the present paper a generalized Kählerian space GK 2 N of the second kind is defined, as a GRN with almost complex structure F h i, that is covariantly constant with respect to the second kind of covariant derivative (equation (2.3)). Several theorems are proved. These theorems are generalizations of the corresponding theorems relating to KN. The relations between F h i and four curvature tensors from GRN are obtained.

MODELING CONOID SURFACES

Abstract. In this paper we consider conoid surfaces as frequently used surfaces in building techniques, mainly as daring roof structures. Different types of conoids are presented using the programme package Mathematica. We describe the generation of conoids and by means of parametric representation we get their graphics. The geometric approach offers a wide range of possibilities in the research of complicated spatial surface systems

Two Invariants for Geometric Mappings

Two invariants for mappings of affine connection spaces with a special form of deformation tensors are obtained in this paper. We used the methodology of Vesić to obtain the form of these invariants. At the end of this paper, we used these forms to obtain two invariants for third-type almost-geodesic mappings of symmetric affine connection

Basic equations of GG-almost geodesic mappings of the second type, which have the property of reciprocity

summary:We study $G$-almost geodesic mappings of the second type $\underset \theta \to \pi _2(e)$, $\theta =1,2$ between non-symmetric affine connection spaces. These mappings are a generalization of the second type almost geodesic mappings defined by N. S. Sinyukov (1979). We investigate a special type of these mappings in this paper. We also consider $e$-structures that generate mappings of type $\underset \theta \to \pi _2(e)$, $\theta =1,2$. For a mapping $\underset \theta \to \pi _2(e,F)$, $\theta =1,2$, we determine the basic equations which generate them