Curvature homogeneous spaces whose curvature tensors have large symmetries

Tsukada, Kazumi. "Curvature homogeneous spaces whose curvature tensors have large symmetries." Commentationes Mathematicae Universitatis Carolinae 43.2 (2002): 283-297. <http://eudml.org/doc/248970>.

@article{Tsukada2002,
abstract = {We study curvature homogeneous spaces or locally homogeneous spaces whose curvature tensors are invariant by the action of “large" Lie subalgebras $\mathfrak \{h\}$ of $\mathfrak \{so\}(n)$. In this paper we deal with the cases of $\mathfrak \{h\}=\mathfrak \{so\}(r) \oplus \mathfrak \{so\}(n-r)$$(2\le r \le n-r)$, $\mathfrak \{so\}(n-2)$, and the Lie algebras of Lie groups acting transitively on spheres, and classify such curvature homogeneous spaces or locally homogeneous spaces.},
author = {Tsukada, Kazumi},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {locally homogeneous spaces; curvature homogeneous spaces; totally geodesic foliations; locally homogeneous spaces; curvature homogeneous spaces; totally geodesic foliations},
language = {eng},
number = {2},
pages = {283-297},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Curvature homogeneous spaces whose curvature tensors have large symmetries},
url = {http://eudml.org/doc/248970},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Tsukada, Kazumi
TI - Curvature homogeneous spaces whose curvature tensors have large symmetries
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 2
SP - 283
EP - 297
AB - We study curvature homogeneous spaces or locally homogeneous spaces whose curvature tensors are invariant by the action of “large" Lie subalgebras $\mathfrak {h}$ of $\mathfrak {so}(n)$. In this paper we deal with the cases of $\mathfrak {h}=\mathfrak {so}(r) \oplus \mathfrak {so}(n-r)$$(2\le r \le n-r)$, $\mathfrak {so}(n-2)$, and the Lie algebras of Lie groups acting transitively on spheres, and classify such curvature homogeneous spaces or locally homogeneous spaces.
LA - eng
KW - locally homogeneous spaces; curvature homogeneous spaces; totally geodesic foliations; locally homogeneous spaces; curvature homogeneous spaces; totally geodesic foliations
UR - http://eudml.org/doc/248970
ER -

References

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