We define and study both neutral slant and semineutral slant submanifolds of an almost para-Hermitian manifold and, in particular, of a para-Kähler manifold. We give characterization theorems for neutral slant and semi-neutral slant submanifolds. We also investigate the integrability conditions for the distributions involved in the definition of a semi-neutral slant submanifold when the ambient manifold is a para-Kähler manifold.
References
B.-Y. Chen, “Slant immersions,” Bulletin of the Australian Mathematical Society, vol. 41, no. 1, pp. 135–147, 1990. MR1043974 0677.53060 10.1017/S0004972700017925 B.-Y. Chen, “Slant immersions,” Bulletin of the Australian Mathematical Society, vol. 41, no. 1, pp. 135–147, 1990. MR1043974 0677.53060 10.1017/S0004972700017925
B.-Y. Chen, Geometry of Slant Submanifolds, Katholieke Universiteit Leuven, Louvain, Belgium, 1990. MR1099374 0677.53060 B.-Y. Chen, Geometry of Slant Submanifolds, Katholieke Universiteit Leuven, Louvain, Belgium, 1990. MR1099374 0677.53060
M. Atçeken, “Semi-slant submanifolds of an almost paracontact metric manifold,” Canadian Mathematical Bulletin, vol. 53, no. 2, pp. 206–217, 2010. MR2662683 10.4153/CMB-2010-003-0 M. Atçeken, “Semi-slant submanifolds of an almost paracontact metric manifold,” Canadian Mathematical Bulletin, vol. 53, no. 2, pp. 206–217, 2010. MR2662683 10.4153/CMB-2010-003-0
H. Li and X. Liu, “Semineutral Slant Submanifolds of Almost Para-Hermitian Manifolds,” Georgian Mathematical Journal, vol. 12, no. 2, pp. 273–282, 2005. MR2174183 1093.53025 H. Li and X. Liu, “Semineutral Slant Submanifolds of Almost Para-Hermitian Manifolds,” Georgian Mathematical Journal, vol. 12, no. 2, pp. 273–282, 2005. MR2174183 1093.53025
B. Şahin and S. Keleş, “Slant submanifolds of Kaehler product manifolds,” Turkish Journal of Mathematics, vol. 31, no. 1, pp. 65–77, 2007. MR2311604 1126.53018 B. Şahin and S. Keleş, “Slant submanifolds of Kaehler product manifolds,” Turkish Journal of Mathematics, vol. 31, no. 1, pp. 65–77, 2007. MR2311604 1126.53018
N. Papaghiuc, “Semi-slant submanifolds of a Kaehlerian manifold,” Analele Ştiinţifice ale Universităţii Al. I. Cuza din Iaşi. Serie Nouă. Matematică, vol. 40, no. 1, pp. 55–61, 1994. MR1328947 0847.53012 N. Papaghiuc, “Semi-slant submanifolds of a Kaehlerian manifold,” Analele Ştiinţifice ale Universităţii Al. I. Cuza din Iaşi. Serie Nouă. Matematică, vol. 40, no. 1, pp. 55–61, 1994. MR1328947 0847.53012
A. Lotta, “Slant submanifolds in contact geometry,” Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie, vol. 39, pp. 183–198, 1996. A. Lotta, “Slant submanifolds in contact geometry,” Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie, vol. 39, pp. 183–198, 1996.
A. Lotta, “Three-dimensional slant submanifolds of $K$-contact manifolds,” Balkan Journal of Geometry and its Applications, vol. 3, no. 1, pp. 37–51, 1998. MR1664499 A. Lotta, “Three-dimensional slant submanifolds of $K$-contact manifolds,” Balkan Journal of Geometry and its Applications, vol. 3, no. 1, pp. 37–51, 1998. MR1664499
J. L. Cabrerizo, A. Carriazo, L. M. Fernández, and M. Fernández, “Slant submanifolds in Sasakian manifolds,” Glasgow Mathematical Journal, vol. 42, no. 1, pp. 125–138, 2000. MR1739684 0957.53022 J. L. Cabrerizo, A. Carriazo, L. M. Fernández, and M. Fernández, “Slant submanifolds in Sasakian manifolds,” Glasgow Mathematical Journal, vol. 42, no. 1, pp. 125–138, 2000. MR1739684 0957.53022
J. L. Cabrerizo, A. Carriazo, L. M. Fernández, and M. Fernández, “Semi-slant submanifolds of a Sasakian manifold,” Geometriae Dedicata, vol. 78, no. 2, pp. 183–199, 1999. MR1722833 0944.53028 10.1023/A:1005241320631 J. L. Cabrerizo, A. Carriazo, L. M. Fernández, and M. Fernández, “Semi-slant submanifolds of a Sasakian manifold,” Geometriae Dedicata, vol. 78, no. 2, pp. 183–199, 1999. MR1722833 0944.53028 10.1023/A:1005241320631
K. Arslan, A. Carriazo, B.-Y. Chen, and C. Murathan, “On slant submanifolds of neutral Kaehler manifolds,” Taiwanese Journal of Mathematics, vol. 14, no. 2, pp. 561–584, 2010. MR2655787 1202.53022 K. Arslan, A. Carriazo, B.-Y. Chen, and C. Murathan, “On slant submanifolds of neutral Kaehler manifolds,” Taiwanese Journal of Mathematics, vol. 14, no. 2, pp. 561–584, 2010. MR2655787 1202.53022
V. Cruceanu, P. Fortuny, and P. M. Gadea, “A survey on paracomplex geometry,” The Rocky Mountain Journal of Mathematics, vol. 26, no. 1, pp. 83–115, 1996. MR1386154 0856.53049 10.1216/rmjm/1181072105 euclid.rmjm/1181072105
V. Cruceanu, P. Fortuny, and P. M. Gadea, “A survey on paracomplex geometry,” The Rocky Mountain Journal of Mathematics, vol. 26, no. 1, pp. 83–115, 1996. MR1386154 0856.53049 10.1216/rmjm/1181072105 euclid.rmjm/1181072105
S. Ivanov and S. Zamkovoy, “Parahermitian and paraquaternionic manifolds,” Differential Geometry and Its Applications, vol. 23, no. 2, pp. 205–234, 2005. MR2158044 10.1016/j.difgeo.2005.06.002 S. Ivanov and S. Zamkovoy, “Parahermitian and paraquaternionic manifolds,” Differential Geometry and Its Applications, vol. 23, no. 2, pp. 205–234, 2005. MR2158044 10.1016/j.difgeo.2005.06.002