scholarly journals New integrability conditions of derivational equations of a submanifold in a generalized Riemannian space

Filomat ◽  
2010 ◽  
Vol 24 (4) ◽  
pp. 137-146 ◽  
Author(s):  
Svetislav Mincic ◽  
Ljubica Velimirovic ◽  
Mica Stankovic
Keyword(s):  
Covariant Derivative ◽  
Riemannian Space ◽  
Generalized Riemannian Space ◽  
Integrability Conditions ◽  
Codazzi Equations

The present work is a continuation of [5] and [6]. In [5] we have obtained derivational equations of a submanifold XM of a generalized Riemannian space GRN. Since the basic tensor in GRN is asymmetric and in this way the connection is also asymmetric, in a submanifold the connection is generally asymmetric too. By reason of this, we define 4 kinds of covariant derivative and obtain 4 kinds of derivational equations. In [6] we have obtained integrability conditions and Gauss-Codazzi equations using the 1st and the 2st kind of covariant derivative. The present work deals in the cited matter, using the 3rd and the 4th kind of covariant derivative. One obtains three new integrability conditions for derivational equations of tangents and three such conditions for normals of the submanifold, as the corresponding Gauss-Codazzi equations too.

scholarly journals Some relations in the generalized Kählerian spaces of the second kind

Filomat ◽  
2009 ◽  
Vol 23 (2) ◽  
pp. 82-89 ◽  
Author(s):  
Mica Stankovic ◽  
Ljubica Velimirovic ◽  
Milan Zlatanovic
Keyword(s):  
Covariant Derivative ◽  
Riemannian Space ◽  
Complex Structure ◽  
Almost Complex Structure ◽  
Generalized Riemannian Space ◽  
Almost Complex ◽  
Definition Of ◽  
Curvature Tensors

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 K?hlerian space GK2 N of the second kind is defined, as a GRN with almost complex structure Fhi, 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 Fhi and four curvature tensors from GRN are obtained.

scholarly journals On integrability conditions of derivation equations in a subspace of asymmetric affine connection space

Filomat ◽  
2015 ◽  
Vol 29 (10) ◽  
pp. 2421-2427
Author(s):  
Milan Zlatanovic ◽  
Svetislav Mincic ◽  
Ljubica Velimirovic
Keyword(s):  
Covariant Derivative ◽  
Affine Connection ◽  
Integrability Conditions ◽  
Connection Space ◽  
Codazzi Equations

In a space LN of asymmetric affine connection by equations (1.1) a submanifold XM ? LN is defined. On XM and on pseudonormal submanifold NXN-M asymmetric induced connections are defined. Because of asymmetry of induced connection it is possible to define four kinds of covariant derivative. In this work we are considering integrability conditions of derivational equations [4] obtained by help of the 1st and the 2nd kind of covariant derivative. The corresponding Gauss-Codazzi equations are obtained too.

scholarly journals Conformal Equitorsion and Concircular Transformations in a Generalized Riemannian Space

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 61
Author(s):  
Ana M. Velimirović
Keyword(s):  
Riemannian Space ◽  
Conformal Transformations ◽  
Generalized Riemannian Space ◽  
Basic Facts ◽  
In The Beginning ◽  
Curvature Tensors

In the beginning, the basic facts about a conformal transformations are exposed and then equitorsion conformal transformations are defined. For every five independent curvature tensors in Generalized Riemannian space, the above cited transformations are investigated and corresponding invariants-5 concircular tensors of concircular transformations are found.

scholarly journals Conformal curvature tensors in a generalized Riemannian space in Eisenhart sense

2020 ◽  
pp. 34-34
Author(s):  
Ana Velimirovic
Keyword(s):  
Curvature Tensor ◽  
Riemannian Space ◽  
Conformal Transformation ◽  
Conformal Curvature ◽  
Conformal Curvature Tensor ◽  
Generalized Riemannian Space ◽  
Curvature Tensors ◽  
Special Case

In the present paper generalizations of conformal curvature tensor from Riemannian space are given for five independent curvature tensors in generalized Riemannian space (GRN ), i.e. when the basic tensor is non-symmetric. In earlier works of S. Mincic and M. Zlatanovic et al a special case has been investigated, that is the case when in the conformal transformation the torsion remains invariant (equitorsion transformation). In the present paper this condition is not supposed and for that reason the results are more general and new.

scholarly journals Second type almost geodesic mappings of special class and their invariants

Filomat ◽  
2019 ◽  
Vol 33 (4) ◽  
pp. 1201-1208
Author(s):  
Nenad Vesic ◽  
Mica Stankovic
Keyword(s):  
Riemannian Space ◽  
Special Class ◽  
Generalized Riemannian Space ◽  
Special Case

Invariants of almost geodesic mappings of a generalized Riemannian space are discussed in this paper. As a special case, invariants of equitorsion almost geodesic mappings of this type are discussed in here.

scholarly journals Infinitesimal deformations of basic tensor in generalized Riemannian space

Filomat ◽  
2007 ◽  
Vol 21 (2) ◽  
pp. 235-242 ◽  
Author(s):  
Ljubica Velimirovic ◽  
S.M. Mincic ◽  
M.S. Stankovic
Keyword(s):  
Riemannian Space ◽  
Lie Derivatives ◽  
Generalized Riemannian Space ◽  
Infinitesimal Deformations ◽  
Basic Facts

At the beginning of the present work the basic facts on generalized Riemannian space (GRn) in the sense of Eisenhart's definition [Eis] and also on infinitesimal deformations of a space are given. We study the Lie derivatives and infinitesimal deformations of basic covariant and contravariant tensor at GRn.

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