Geodesic mapping onto Kählerian spaces of the first kind

Milan Zlatanović; Irena Hinterleitner; Marija Najdanović

Czechoslovak Mathematical Journal (2014)

  • Volume: 64, Issue: 4, page 1113-1122
  • ISSN: 0011-4642

Abstract

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In the present paper a generalized Kählerian space 𝔾 𝕂 1 N of the first kind is considered as a generalized Riemannian space 𝔾ℝ N with almost complex structure F i h that is covariantly constant with respect to the first kind of covariant derivative. Using a non-symmetric metric tensor we find necessary and sufficient conditions for geodesic mappings f : 𝔾ℝ N → 𝔾 𝕂 ¯ 1 N with respect to the four kinds of covariant derivatives. These conditions have the form of a closed system of partial differential equations in covariant derivatives with respect to unknown components of the metric tensor and the complex structure of the Kählerian space 𝔾 𝕂 1 N .

How to cite

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Zlatanović, Milan, Hinterleitner, Irena, and Najdanović, Marija. "Geodesic mapping onto Kählerian spaces of the first kind." Czechoslovak Mathematical Journal 64.4 (2014): 1113-1122. <http://eudml.org/doc/269829>.

@article{Zlatanović2014,
abstract = {In the present paper a generalized Kählerian space $\mathbb \{G\} \{\underset\{1\}\{\mathbb \{K\}\}_N\}$ of the first kind is considered as a generalized Riemannian space $\mathbb \{GR\}_N$ with almost complex structure $\smash\{F^h_i\}$ that is covariantly constant with respect to the first kind of covariant derivative. Using a non-symmetric metric tensor we find necessary and sufficient conditions for geodesic mappings $f\colon \mathbb \{GR\}_N\rightarrow \mathbb \{G\}\underset\{1\}\{\mathbb \{\overline\{K\}\}\}_N$ with respect to the four kinds of covariant derivatives. These conditions have the form of a closed system of partial differential equations in covariant derivatives with respect to unknown components of the metric tensor and the complex structure of the Kählerian space $\mathbb \{G\}\{\underset\{1\}\{\mathbb \{K\}\}\}_N$.},
author = {Zlatanović, Milan, Hinterleitner, Irena, Najdanović, Marija},
journal = {Czechoslovak Mathematical Journal},
keywords = {geodesic mapping; equitorsion geodesic mapping; generalized Kählerian space; geodesic mapping; equitorsion geodesic mapping; generalized Kählerian space},
language = {eng},
number = {4},
pages = {1113-1122},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Geodesic mapping onto Kählerian spaces of the first kind},
url = {http://eudml.org/doc/269829},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Zlatanović, Milan
AU - Hinterleitner, Irena
AU - Najdanović, Marija
TI - Geodesic mapping onto Kählerian spaces of the first kind
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 4
SP - 1113
EP - 1122
AB - In the present paper a generalized Kählerian space $\mathbb {G} {\underset{1}{\mathbb {K}}_N}$ of the first kind is considered as a generalized Riemannian space $\mathbb {GR}_N$ with almost complex structure $\smash{F^h_i}$ that is covariantly constant with respect to the first kind of covariant derivative. Using a non-symmetric metric tensor we find necessary and sufficient conditions for geodesic mappings $f\colon \mathbb {GR}_N\rightarrow \mathbb {G}\underset{1}{\mathbb {\overline{K}}}_N$ with respect to the four kinds of covariant derivatives. These conditions have the form of a closed system of partial differential equations in covariant derivatives with respect to unknown components of the metric tensor and the complex structure of the Kählerian space $\mathbb {G}{\underset{1}{\mathbb {K}}}_N$.
LA - eng
KW - geodesic mapping; equitorsion geodesic mapping; generalized Kählerian space; geodesic mapping; equitorsion geodesic mapping; generalized Kählerian space
UR - http://eudml.org/doc/269829
ER -

References

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