Codimension 2 submanifolds of paracosymplectic manifolds with normal Reeb vector field

被引:0
作者
Bejan, Cornelia-Livia [1 ]
Nakova, Galia [2 ]
机构
[1] Gh Asachi Tech Univ Iasi, Dept Math, B Dul Carol I, Iasi 700506, Romania
[2] St Cyril & St Methodius Univ Veliko Tarnovo, Fac Math & Informat, Dept Algebra & Geometry, 2 Teodosii Tarnovski Str, Veliko Tarnovo 5003, Bulgaria
关键词
Submanifold; Almost paracontact metric manifold; Paracosymplectic manifold; Para-Sasakian manifold; PARACONTACT;
D O I
10.2298/FIL2325693B
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This study is devoted to a submanifold M of codimension 2 of an almost paracontact metric manifold M, for which the Reeb vector field of the ambient manifold is normal. Some sufficient conditions for the existence of M are given. When M is paracosymplectic, then some necessary and sufficient conditions are established for M to fall in one of the following classes of almost paracontact metric manifolds according to the classification given by S. Zamkovoy and G. Nakova: normal, paracontact metric, paraSasakian, K-paracontact, quasi-para-Sasakian, respectively. When in addition, M is para-Sasakian and M is paracosymplectic, some characterization results are obtained for M to be totally umbilical, as well as a nonexistence result for M to be totally geodesic is provided. The case when M is of a constant sectional curvature is analysed and an example is constructed.
引用
收藏
页码:8693 / 8707
页数:15
相关论文
共 15 条
[1]  
[Anonymous], 1992, Math. J. Toyama Univ.
[2]  
[Anonymous], 1996, DIFF GEOM APPL BRNO
[3]   Legendre Curves on Generalized Paracontact Metric Manifolds [J].
Bejan, Cornelia-Livia ;
Eken Meric, Semsi ;
Kilic, Erol .
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2019, 42 (01) :185-199
[4]  
Blair DE, 2010, PROG MATH, V203, P1, DOI 10.1007/978-0-8176-4959-3
[5]  
DACKO P, 2004, TSUKUBA J MATH, V28, P193
[6]   Para-Sasaki-like Riemannian manifolds and new Einstein metrics [J].
Ivanov, Stefan ;
Manev, Hristo ;
Manev, Mancho .
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2021, 115 (03)
[7]  
Kanemaki S., 1984, BANACH CTR PUBLICATI, V12
[8]   ALMOST PARACONTACT AND PARAHODGE STRUCTURES ON MANIFOLDS [J].
KANEYUKI, S ;
WILLIAMS, FL .
NAGOYA MATHEMATICAL JOURNAL, 1985, 99 (SEP) :173-187
[9]  
KANEYUKI S, 1985, TOKYO J MATH, V8, P81, DOI DOI 10.3836/TJM/1270151571
[10]  
Nakova G., 1997, Math. Balkanica (N.S.), V11, P255