Öz
A Lorentzian para-Sasakian (LP-Sasakian) space form is a kind of para-Sasakian manifold with constant $ \varphi- $ holomorphic sectional curvature. The presented paper is on the curvatures of semi-invariant submanifolds of a LP-Sasakian space form. Firstly, the definition of a semi-invariant submanifold of LP-Sasakian space form is given and an example is presented. Then, using Gauss equation related to curvatures used for obtaining some important results on Ricci and scalar curvatures. Moreover, by suffering from these results conditions of distributions being Einstein have been examined. Finally, semi-invariant products of Lorentzian para-Sasakian manifolds have been considered and an important inequality for second fundamental form is proved.
Anahtar Kelimeler
Lorentzian para-Sasakian manifold Lorentzian para-Sasakian space forms semi-invariant submanifold
Kaynakça
- Adati T., Matsumoto, K., On conformally recurrent and conformally symmetric P-Sasakian manifolds, TRU Mathematics, 13(1997), 25–32.
- Alegre, P., Semi-invariant submanifolds of Lorentzian Sasakian manifolds, Demonstratio Mathematica, XLIV(2)(2011), 391–406.
- Aqeel, A.A., De, U.C., Ghosh, G.C., On Lorentzian para-Sasakian manifolds, Kuwait Journal of Science and Engineering, 31(2)(2004), 1–13.
- De, U.C., Matsumoto, K., Shaikh, A.A., On Lorentzian para-Sasakian manifolds, Rendiconti del Seminario matematico di Messina, 3(1999), 149–156.
- Devi, M.S., Sangi, B., Tluangi, H., Siami, K., Khawlhring, L. et al., Some curvature properties on Lorentzian para-sasakian manifolds, Advances and Applications in Mathematical Sciences, 21(6)(2022), 3191–31200.
- Duggal, K.L., Space time manifold and contact Manifolds, International Journal of Mathematics and Mathematical Sciences, 13(1990), 545–554.
- Ikawa, T., Erdogan, M., Sasakian manifolds with Lorentzian metric, Kyungpook Mathematical Journal, 35(1996), 517–526
- Ikawa, T., Spacelike maximal surfaces with constant scalar normal curvature in a normal contact Lorentzian manifold, Bulletin of the Malaysian Mathematical Sciences Society, 21(1998), 31–36.
- Laha, B., D-homothodics deformations of Lorentzian para Sasakian manifolds, International Journal of Mathematical Combinatorics, 2(2019), 34–42.
- Matsumoto, K., On Lorentzian para-contact manifolds, Bulletin of the Yamagata University. Natural Science, 12(1989), 151–156.
- Mihai I., Rosca, R., On Lorentzian P-Sasakian manifolds, Classical Analysis, World Scientific Publication, Singapore, (1992), 155–169.
- Mihai, I., De, U.C., Shaikh, A.A., On Lorentzian para-Sasakian manifolds, The Korean Journal of Mathematics, 6(1999), 1–13.
- Pandey, S., Singh, A., Certain results of Ricci soliton on 3-dimensional Lorentzian para α-Sasakian manifolds, International Journal of Maps in Mathematics, 5(2)(2022), 139–153.
- Sato, I., On a structure similar to the almost contact structure Tensor (N.S.), 30(1976), 219–224.
- Takahashi, T., Sasakian manifold with pseudo-Riemannian metric, Tohoku Mathematical Journal, 21(2)(1969), 271–290.
- Tanno, S., Sasakian manifolds with constant ’φ-holomorphic sectional curvature, Tohoku Mathematical Journal, 21(2)(1969), 501–507.
- Venkatesha, V., Basavarajappa, S., Invariant submanifolds of LP-Sasakian manifolds, Journal of Mathematics, 6(1)(2020), 16–26.
Öz
Kaynakça
- Adati T., Matsumoto, K., On conformally recurrent and conformally symmetric P-Sasakian manifolds, TRU Mathematics, 13(1997), 25–32.
- Alegre, P., Semi-invariant submanifolds of Lorentzian Sasakian manifolds, Demonstratio Mathematica, XLIV(2)(2011), 391–406.
- Aqeel, A.A., De, U.C., Ghosh, G.C., On Lorentzian para-Sasakian manifolds, Kuwait Journal of Science and Engineering, 31(2)(2004), 1–13.
- De, U.C., Matsumoto, K., Shaikh, A.A., On Lorentzian para-Sasakian manifolds, Rendiconti del Seminario matematico di Messina, 3(1999), 149–156.
- Devi, M.S., Sangi, B., Tluangi, H., Siami, K., Khawlhring, L. et al., Some curvature properties on Lorentzian para-sasakian manifolds, Advances and Applications in Mathematical Sciences, 21(6)(2022), 3191–31200.
- Duggal, K.L., Space time manifold and contact Manifolds, International Journal of Mathematics and Mathematical Sciences, 13(1990), 545–554.
- Ikawa, T., Erdogan, M., Sasakian manifolds with Lorentzian metric, Kyungpook Mathematical Journal, 35(1996), 517–526
- Ikawa, T., Spacelike maximal surfaces with constant scalar normal curvature in a normal contact Lorentzian manifold, Bulletin of the Malaysian Mathematical Sciences Society, 21(1998), 31–36.
- Laha, B., D-homothodics deformations of Lorentzian para Sasakian manifolds, International Journal of Mathematical Combinatorics, 2(2019), 34–42.
- Matsumoto, K., On Lorentzian para-contact manifolds, Bulletin of the Yamagata University. Natural Science, 12(1989), 151–156.
- Mihai I., Rosca, R., On Lorentzian P-Sasakian manifolds, Classical Analysis, World Scientific Publication, Singapore, (1992), 155–169.
- Mihai, I., De, U.C., Shaikh, A.A., On Lorentzian para-Sasakian manifolds, The Korean Journal of Mathematics, 6(1999), 1–13.
- Pandey, S., Singh, A., Certain results of Ricci soliton on 3-dimensional Lorentzian para α-Sasakian manifolds, International Journal of Maps in Mathematics, 5(2)(2022), 139–153.
- Sato, I., On a structure similar to the almost contact structure Tensor (N.S.), 30(1976), 219–224.
- Takahashi, T., Sasakian manifold with pseudo-Riemannian metric, Tohoku Mathematical Journal, 21(2)(1969), 271–290.
- Tanno, S., Sasakian manifolds with constant ’φ-holomorphic sectional curvature, Tohoku Mathematical Journal, 21(2)(1969), 501–507.
- Venkatesha, V., Basavarajappa, S., Invariant submanifolds of LP-Sasakian manifolds, Journal of Mathematics, 6(1)(2020), 16–26.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Yapay Zeka (Diğer), Cebirsel ve Diferansiyel Geometri |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Aralık 2023 |
| Yayımlandığı Sayı | Yıl 2023 Cilt: 15 Sayı: 2 |