Öz
Bu makalenin asıl amacı alfa Kenmotsu psödo metrik manifoldlar üzerinde bazı eğrilik özelliklerini incelemektir. Özellikle bu tür manifoldlar üzerinde lokal simetri, global ϕ-simetri ve lokal ϕ-simetri gibi tensör koşulları bazı ek şartlar altında göz önüne alınmıştır. Ayrıca, η-Einstein ve Einstein manifoldlar için gerek ve yeter koşullar çalışılmıştır. Bundan başka, ξ-kesit ve ϕ-kesit eğrilikleri ile ilgili bazı sonuçlar alfa Kenmotsu psödo metrik manifoldlar üzerinde verilmiştir. Son olarak, makale alfa Kenmotsu psödo metrik manifoldlar için açıklayıcı bir örnekle sonlandırılmıştır.
Anahtar Kelimeler
Alfa Kenmotsu manifold psödo metrik sabit eğrilik kesit eğriliği
Destekleyen Kurum
Afyon Kocatepe Üniversitesi Bilimsel Araştırma Projeleri Koordinasyon Birimi
Proje Numarası
17.FEN.BİL.11
Teşekkür
Bu çalışma, Afyon Kocatepe Üniversitesi Bilimsel Araştırma Projeleri Koordinasyon Birimi tarafından 17.FEN.BİL.11 numaralı proje ile desteklenmiştir. Ayrıca, yapıcı yorumları ve katkılarından dolayı saygıdeğer hakemlere teşekkür ederiz.
Kaynakça
- Alegre, P., 2011. Semi invariant submanifolds of Lorentzian Sasakian manifolds. Demonstratio Mathematica, 44, 391–406.
- Calvaruso, G., 2011. Contact Lorentzian manifolds. Differential Geometry and its Applications, 29, 541–551.
- Calvaruso, G. and Perrone, D., 2010. Contact pseudo-metric manifolds. Differential Geometry and its Applications, 28, 615–634.
- Dileo, G. and Pastore, A. M., 2009. Almost Kenmotsu manifolds with a condition of η-parallelism. Differential Geometry and its Applications, 27, 671–679.
- Duggal, K.L., 1990. Space time manifolds and contact structures. Internat. J. Math. & Math. Sci, 13, 545–554.
- Kenmotsu, K., 1972. A class of contact Riemannian manifold, Tôhoku Math. Journal, 24 , 93–103.
- O’Neil, B., 1983, Semi-Riemannian geometry with applications to relativity, Academic Press, New York.
- Öztürk, H., 2016. On Almost α-Kenmotsu Manifolds with Some Tensor Fields, AKU J. Sci. Eng., 16, 256–264.
- Öztürk, H., Aktan N. and Murathan C., 2010. On α-Kenmotsu manifolds satisfying certain conditions. Applied Sciences, 12, 115–126.
- Perrone, D., 2014. Contact pseudo-metric manifolds of constant curvature and CR geometry. Results in Mathematics, 66, 213–225.
- Takahashi, T., 1969. Sasakian manifold with pseudo-Riemannian manifolds. Tôhoku Math. Journal, 21, 271–290.
- Yano, K. and Kon, M., 1984, Structures on manifolds, Series in Pure Mathematics, 3. World Scientific Publishing Co., Singapore.
- Wang, Y. and Liu, X., 2016. Almost Kenmotsu pseudo-metric manifolds. Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica, 62, 241–256.
Öz
The aim of this paper is to investigate some curvature properties on alpha Kenmotsu pseudo metric manifolds. In particular, the tensor conditions such as locally symmetry, globally ϕ-symmetry and locally ϕ-symmetry under some additional conditions on such manifolds are considered. Also, the necessary and sufficient conditions for η-Einstein and Einstein manifolds are studied. Furthermore, some results are related to ξ-sectional and ϕ-sectional curvatures on alpha Kenmotsu pseudo metric manifolds are given. Finally, the paper is concluded with an illustrative example for alpha Kenmotsu pseudo metric manifolds.
Anahtar Kelimeler
Alpha Kenmotsu manifold Pseudo metric Constant curvature Sectional curvature
Proje Numarası
17.FEN.BİL.11
Kaynakça
- Alegre, P., 2011. Semi invariant submanifolds of Lorentzian Sasakian manifolds. Demonstratio Mathematica, 44, 391–406.
- Calvaruso, G., 2011. Contact Lorentzian manifolds. Differential Geometry and its Applications, 29, 541–551.
- Calvaruso, G. and Perrone, D., 2010. Contact pseudo-metric manifolds. Differential Geometry and its Applications, 28, 615–634.
- Dileo, G. and Pastore, A. M., 2009. Almost Kenmotsu manifolds with a condition of η-parallelism. Differential Geometry and its Applications, 27, 671–679.
- Duggal, K.L., 1990. Space time manifolds and contact structures. Internat. J. Math. & Math. Sci, 13, 545–554.
- Kenmotsu, K., 1972. A class of contact Riemannian manifold, Tôhoku Math. Journal, 24 , 93–103.
- O’Neil, B., 1983, Semi-Riemannian geometry with applications to relativity, Academic Press, New York.
- Öztürk, H., 2016. On Almost α-Kenmotsu Manifolds with Some Tensor Fields, AKU J. Sci. Eng., 16, 256–264.
- Öztürk, H., Aktan N. and Murathan C., 2010. On α-Kenmotsu manifolds satisfying certain conditions. Applied Sciences, 12, 115–126.
- Perrone, D., 2014. Contact pseudo-metric manifolds of constant curvature and CR geometry. Results in Mathematics, 66, 213–225.
- Takahashi, T., 1969. Sasakian manifold with pseudo-Riemannian manifolds. Tôhoku Math. Journal, 21, 271–290.
- Yano, K. and Kon, M., 1984, Structures on manifolds, Series in Pure Mathematics, 3. World Scientific Publishing Co., Singapore.
- Wang, Y. and Liu, X., 2016. Almost Kenmotsu pseudo-metric manifolds. Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica, 62, 241–256.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Konular | Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Proje Numarası | 17.FEN.BİL.11 |
| Yayımlanma Tarihi | 31 Aralık 2020 |
| Gönderilme Tarihi | 1 Ekim 2020 |
| Yayımlandığı Sayı | Yıl 2020 Cilt: 20 Sayı: 6 |
