On Uniqueness Theoremsfor Ricci Tensor

Khripunova, Marina B., et al. "On Uniqueness Theoremsfor Ricci Tensor." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 55.1 (2016): 47-52. <http://eudml.org/doc/286700>.

@article{Khripunova2016,
abstract = {In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold $M$ and a symmetric 2-tensor $r$, construct a metric on $M$ whose Ricci tensor equals $r$. In particular, DeTurck and Koiso proved the following celebrated result: the Ricci curvature uniquely determines the Levi-Civita connection on any compact Einstein manifold with non-negative section curvature. In the present paper we generalize the result of DeTurck and Koiso for a Riemannian manifold with non-negative section curvature. In addition, we extended our result to complete non-compact Riemannian manifolds with nonnegative sectional curvature and with finite total scalar curvature.},
author = {Khripunova, Marina B., Stepanov, Sergey E., Tsyganok, Irina I., Mikeš, Josef},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Uniqueness theorem for Ricci tensor; compact and complete Riemannian manifolds; vanishing theorem},
language = {eng},
number = {1},
pages = {47-52},
publisher = {Palacký University Olomouc},
title = {On Uniqueness Theoremsfor Ricci Tensor},
url = {http://eudml.org/doc/286700},
volume = {55},
year = {2016},
}

TY - JOUR
AU - Khripunova, Marina B.
AU - Stepanov, Sergey E.
AU - Tsyganok, Irina I.
AU - Mikeš, Josef
TI - On Uniqueness Theoremsfor Ricci Tensor
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2016
PB - Palacký University Olomouc
VL - 55
IS - 1
SP - 47
EP - 52
AB - In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold $M$ and a symmetric 2-tensor $r$, construct a metric on $M$ whose Ricci tensor equals $r$. In particular, DeTurck and Koiso proved the following celebrated result: the Ricci curvature uniquely determines the Levi-Civita connection on any compact Einstein manifold with non-negative section curvature. In the present paper we generalize the result of DeTurck and Koiso for a Riemannian manifold with non-negative section curvature. In addition, we extended our result to complete non-compact Riemannian manifolds with nonnegative sectional curvature and with finite total scalar curvature.
LA - eng
KW - Uniqueness theorem for Ricci tensor; compact and complete Riemannian manifolds; vanishing theorem
UR - http://eudml.org/doc/286700
ER -