Riemannian Warped Product Maps
Küçük Resim Yok
Tarih
2024
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Springer Basel Ag
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
In this paper, we introduce Riemannian warped product map as a generalization of warped product isometric immersion and Riemannian warped product submersion with examples and obtain some characterizations. First, we define Riemannian warped product map and find conditions for a Riemannian map to be Riemannian warped product map. We show that Riemannian warped product map is a composition of Riemannian warped product submersion followed by warped product isometric immersion locally. In addition, we show that Riemannian warped product map satisfies the generalized eikonal equation which is a well known bridge between geometrical and physical optics. We also find necessary and sufficient conditions for the fibers, range space of the derivative map of Riemannian warped product map and horizontal distributions to be totally geodesic and minimal. Further, we give some fundamental geometric properties for the study of such smooth maps. Precisely, we construct Gauss formula (second fundamental form), Weingarten formula and tension field. We obtain necessary and sufficient conditions for a Riemannian warped product map to be totally geodesic, harmonic and umbilical. Comparatively, we analyse the obtained results with the existing results for a Riemannian map between Riemannian manifolds.
Açıklama
Anahtar Kelimeler
Riemannian Warped Product Manifold, Second Fundamental Form, Riemannian Map, Totally Geodesic Map, Harmonic Map, Umbilical Map
Kaynak
Results In Mathematics
WoS Q Değeri
N/A
Scopus Q Değeri
Q2
Cilt
79
Sayı
2
