On Indefinite locally conformal cosymplectic manifolds
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We prove that there exist foliations whose leaves are the maximal integral null manifolds immersed as submanifolds of indefinite locally conformal cosymplectic manifolds. Necessary and sufficient conditions for such leaves to be screen conformal, as well as possessing integrable distributions are given. Using Newton transformations, we show that any compact ascreen null leaf with a symmetric Ricci tensor admits a totally geodesic screen distribution. Supporting examples are also obtained.
Abstract
We prove that there exist foliations whose leaves are the maximal integral null manifolds immersed as submanifolds of indefinite locally conformal cosymplectic manifolds. Necessary and sufficient conditions for such leaves to be screen conformal, as well as possessing integrable distributions are given. Using Newton transformations, we show that any compact ascreen null leaf with a symmetric Ricci tensor admits a totally geodesic screen distribution. Supporting examples are also obtained.
참고문헌 (17)
- K. Andrzejewski, "Generalized Newton transformation and its applications to extrinsic geometry", Asian J. Math, 20(2), pp.293~322 (2016)
- K. Andrzejewski, "The Newton transformation and new integral formulae for foliated manifolds", Ann. Global Anal. Geom, 37(2), pp.103~111 (2010)
- D. E. Blair, "Riemannian Geometry of Contact and Symplectic Manifolds", Progress in Mathematics, 203 (2002), Birkh¨user
- M. Capursi, "On manifolds admitting metrics which are locally conformal to cosymplectic metrics: their canonical foliations, Boothby-Wang fiberings, and real homology type", Colloq. Math, 61(4), pp.29~40 (1993)
- D. Chinea, "Conformal changes of almost cosymplectic manifolds", Demonstratio Math, 25(3), pp.641~656 (1992)
- J. Dong, "Totally umbilical lightlike hypersurfaces in Robertson-Walker spacetimes", ISRN Geom, 2014, pp.10~ (2014)
- S. Dragomir, "Indefinite locally conformal K¨ahler manifolds", Differential Geom. Appl, 25(1), pp.8~22 (2007)
- K. L. Duggal, "Lightlike submanifolds of semi-Riemannian manifolds and applications, Mathematics and Its Applications" (1996), Kluwer Publishers
- K. L. Duggal, "Differential Geometry of Lightlike Submanifolds, Frontiers in Mathematics" (2010), Birkh¨auser Verlag
- S. I. Goldberg, "Integrability of almost cosymplectic structures", Pacific J. Math, 31, pp.373~382 (1969)
- Dae Ho Jin, "Ascreen lightlike hypersurfaces of a semi-Riemannian space form with a semi-symmetric non-metric connection", 대한수학회논문집, 29(2), pp.311~317 (2014), 대한수학회
- D. N. Kupeli, "Singular semi-Riemannian geometry", Mathematics and Its Applications, 366 (1996), Kluwer Academic Publishers
- Fortuné Massamba, "A Class of Locally Conformal Almost Cosymplectic Manifolds", Bulletin of the Malaysian Mathematical Sciences Society (2016), Springer Nature[DOI]
- F. Massamba, "Quasi generalized CR-lightlike submanifolds of indefinite nearly Sasakian manifolds", Arab. J. Math, 5(2), pp.87~101 (2016)
- Z. Olszak, "On almost cosymplectic manifolds", Kodai Math. J, 4(2), pp.239~250 (1981)
- Z. Olszak, "Locally conformal almost cosymplectic manifolds", Colloq. Math, 57(1), pp.73~87 (1989)
- I. Vaisman, "Conformal changes of almost contact metric structures, Geometry and differential geometry (Proc. Conf., Univ. Haifa, Haifa, 1979)", Lecture Notes in Math., 792, pp.435~443 (1980), Springer