Doubly warped products
Başlık çevirisi mevcut değil.
- Tez No: 400273
- Danışmanlar: PROF. JOHN K. BEEM
- Tez Türü: Doktora
- Konular: Matematik, Mathematics
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 2000
- Dil: İngilizce
- Üniversite: University of Missouri
- Enstitü: Yurtdışı Enstitü
- Ana Bilim Dalı: Matematik Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 138
Özet
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Özet (Çeviri)
In this thesis, we give covariant derivative and curvature formulas of doublyand multiply warped products and consider the geodesic equation on these spaces.We state some basic facts about causality of Lorentzian doubly and multiply warpedproducts and study Cauchy surfaces and global hyperbolicity. We consider null,timelike and spacelike geodesic completeness of Lorentzian doubly and multiplywarped products and again geodesic completeness of these spaces. We give neces-sary conditions for generalized Robertson-Walker space-times with doubly warpedproduct spacial parts to be globally hyperbolic. Moreover, we investigate Lorentziansingly and multiply warped product space-times with positive nonspacelike Riccicurvatures Then we consider Ricci-°at and Einstein Lorentzian singly and multiplywarped products when the ¯bers are Ricci-°at or Einstein. We also state some re-sults for nontrivial doubly warped products to have constant scalar curvature. Wealso state some results about Killing and conformal vector ¯elds of doubly and mul-tiply warped products. Also, we investigate focal and conjugate points of warpedproducts. Finally, we also obtain some solutions to wave equation, eigenvalue prob-lems and Yamabe equation on these spaces.
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