On some relations between curvature and metric tensors in Riemannian spaces

Mikeš, Josef, Laitochová, Jitka, and Pokorná, Olga. "On some relations between curvature and metric tensors in Riemannian spaces." Proceedings of the 19th Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 2000. 173-176. <http://eudml.org/doc/220372>.

@inProceedings{Mikeš2000,
abstract = {The paper generalizes results of H. H. Hacisalihoglu and A. Kh. Amirov [Dokl. Akad. Nauk, Ross. Akad. Nauk 351, No. 3, 295-296 (1996; Zbl 0895.53038) and Sib. Mat. Zh. 39, No. 4, 1005-1012 (1998; Zbl 0913.53019)] on the existence and uniqueness of a Riemannian metric on a domain in $\mathbb \{R\}^n$ given prescribed values for some of the components of the Riemann curvature tensor and initial values of the metric and its partial derivatives. The authors establish the construction (existence and uniqueness) of a metric tensor $g_\{ij\}$ in a semigeodesic coordinate system in a domain $D_n$ in $\mathbb \{R\}^n$ with certain initial conditions on the metric and its partial derivatives $\frac\{ \partial g_\{ij\}\}\{\partial x^1\}$ on a hypersurface, and prescribed values for the components $R_\{1ij1\}$ in $D_n$. The result follows from the existence and uniqueness of solutions of systems of first-order ordinary differential equations.},
author = {Mikeš, Josef, Laitochová, Jitka, Pokorná, Olga},
booktitle = {Proceedings of the 19th Winter School "Geometry and Physics"},
keywords = {Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)},
location = {Palermo},
pages = {173-176},
publisher = {Circolo Matematico di Palermo},
title = {On some relations between curvature and metric tensors in Riemannian spaces},
url = {http://eudml.org/doc/220372},
year = {2000},
}

TY - CLSWK
AU - Mikeš, Josef
AU - Laitochová, Jitka
AU - Pokorná, Olga
TI - On some relations between curvature and metric tensors in Riemannian spaces
T2 - Proceedings of the 19th Winter School "Geometry and Physics"
PY - 2000
CY - Palermo
PB - Circolo Matematico di Palermo
SP - 173
EP - 176
AB - The paper generalizes results of H. H. Hacisalihoglu and A. Kh. Amirov [Dokl. Akad. Nauk, Ross. Akad. Nauk 351, No. 3, 295-296 (1996; Zbl 0895.53038) and Sib. Mat. Zh. 39, No. 4, 1005-1012 (1998; Zbl 0913.53019)] on the existence and uniqueness of a Riemannian metric on a domain in $\mathbb {R}^n$ given prescribed values for some of the components of the Riemann curvature tensor and initial values of the metric and its partial derivatives. The authors establish the construction (existence and uniqueness) of a metric tensor $g_{ij}$ in a semigeodesic coordinate system in a domain $D_n$ in $\mathbb {R}^n$ with certain initial conditions on the metric and its partial derivatives $\frac{ \partial g_{ij}}{\partial x^1}$ on a hypersurface, and prescribed values for the components $R_{1ij1}$ in $D_n$. The result follows from the existence and uniqueness of solutions of systems of first-order ordinary differential equations.
KW - Proceedings; Winter school; Geometry; Physics; Srní (Czech Republic)
UR - http://eudml.org/doc/220372
ER -