- Tytuł:
- A note on geodesic and almost geodesic mappings of homogeneous Riemannian manifolds
- Autorzy:
- Formella, S.
- Powiązania:
- https://bibliotekanauki.pl/articles/255224.pdf
- Data publikacji:
- 2005
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
homogeneous Riemannian manifold
geodesic
almost geodesic
geodesic mapping
almost geodesic mapping - Opis:
- Let M be a differentiable manifold and denote by nabla and nabla~ two linear connections on M. Nabla and nabla~ are said to be geodesically equivalent if and only if they have the same geodesics. A Riemannian manifold (M, g) is a naturally reductive homogeneous manifold if and only if nabla and nabla~ = nabla - T are geodesically equivalent, where T is a homogeneous structure on (M, g) ([7]). In the present paper we prove that if it is possible to map geodesically a homogeneous Riemannian manifold (M, g) onto (M, nabla~), then the map is affine. If a naturally reductive manifold (M, g) admits a nontrivial geodesic mapping onto a Riemannian manifold (formula) then both manifolds are of constant cutvature. We also give some results for almost geodesic mappings (M, g) arr (M, nabla~).
- Źródło:
-
Opuscula Mathematica; 2005, 25, 2; 181-187
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł