Öz
Kaynakça
- Y. Agaoka, I-B. Kim, D.J. Yeom,On doubly warped product manifolds, Mem. Fac. Integrated Arts and Sci., Hiroshimo Univ., ser. IV. 24 (1998), 1-10.
- R.L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Mat. Soc. 145(1) (1969), 1-49.
- R.A. Blumenthal and J.J. Hebda, An analogue of the holonomy bundle for a foliated manifold, Tohoku Math. J. 40(2) (1988), 189-197.
- B.Y. Chen, Geometry of submanifolds and its applicaitons, Science University of Tokyo, Tokyo, 1981.
- B.Y. Chen, Differential geometry of warped product manifolds and submanifolds, World Scientific, 2017.
- P. E. Ehrlich, Metric deformations of Ricci and sectional curvature on compactRiemannian manifolds, Ph.D. dissertation, SUNY, Stony Brook, N.Y., 1974.
- M. Fernandez Lopez , E. Garcia Rio , D.N. Küpeli, B. Ünal, A curvature condition for a twisted product to be a warped product, Manuscripta Math. 106 (2001), 213-217.
- P. Gupta, On compact Einstein doubly warped product manifolds, Tamkang J. Math. 49(4) (2018), 267-275. doi:10.5556/j.tkjm.49.2018.2605.
- G.I. Kruchkovich, On semi-reducible Riemannian spaces (in Russian), Dokl. Akad. Nauk SSSR 115 (1957), 862-865.
- B. Olea, Doubly warped product structures on semi-Riemannian manifolds, Ph.D. thesis, Universty of Malaga, 2009.
- B. O'Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, San Diego, 1983.
- R. Ponge and H. Reckziegel, Twisted products in pseudo- Riemannian geometry, Geom. Dedicata 48 (1993), 15-25.
- B. Ünal, Doubly warped products, Ph.D. thesis, Universty of Missouri-Columbia, 2000.
- K. Yano, M. Kon, Structures on Manifolds, Singapore: World Scientific, 1984.
Öz
We give a new characterization for doubly warped products by using the geometry of their canonical foliations intersecting perpendicularly. We also give a necessary and sufficient condition for a doubly warped product to be a warped or a direct product. As a result, we prove the non-existence of Einstein proper doubly warped product pseudo-Riemannian manifold of dimension grater or equal than 4. .
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Anahtar Kelimeler
Doubly warped product warped product direct product Einstein manifold
Kaynakça
- Y. Agaoka, I-B. Kim, D.J. Yeom,On doubly warped product manifolds, Mem. Fac. Integrated Arts and Sci., Hiroshimo Univ., ser. IV. 24 (1998), 1-10.
- R.L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Mat. Soc. 145(1) (1969), 1-49.
- R.A. Blumenthal and J.J. Hebda, An analogue of the holonomy bundle for a foliated manifold, Tohoku Math. J. 40(2) (1988), 189-197.
- B.Y. Chen, Geometry of submanifolds and its applicaitons, Science University of Tokyo, Tokyo, 1981.
- B.Y. Chen, Differential geometry of warped product manifolds and submanifolds, World Scientific, 2017.
- P. E. Ehrlich, Metric deformations of Ricci and sectional curvature on compactRiemannian manifolds, Ph.D. dissertation, SUNY, Stony Brook, N.Y., 1974.
- M. Fernandez Lopez , E. Garcia Rio , D.N. Küpeli, B. Ünal, A curvature condition for a twisted product to be a warped product, Manuscripta Math. 106 (2001), 213-217.
- P. Gupta, On compact Einstein doubly warped product manifolds, Tamkang J. Math. 49(4) (2018), 267-275. doi:10.5556/j.tkjm.49.2018.2605.
- G.I. Kruchkovich, On semi-reducible Riemannian spaces (in Russian), Dokl. Akad. Nauk SSSR 115 (1957), 862-865.
- B. Olea, Doubly warped product structures on semi-Riemannian manifolds, Ph.D. thesis, Universty of Malaga, 2009.
- B. O'Neill, Semi-Riemannian geometry with applications to relativity, Academic Press, San Diego, 1983.
- R. Ponge and H. Reckziegel, Twisted products in pseudo- Riemannian geometry, Geom. Dedicata 48 (1993), 15-25.
- B. Ünal, Doubly warped products, Ph.D. thesis, Universty of Missouri-Columbia, 2000.
- K. Yano, M. Kon, Structures on Manifolds, Singapore: World Scientific, 1984.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Research Article |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Aralık 2020 |
| Gönderilme Tarihi | 20 Ekim 2019 |
| Kabul Tarihi | 13 Temmuz 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 69 Sayı: 2 |
Kaynak Göster
Cited By
Gradient Solitons on Doubly Warped Product Manifolds
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