Almost(Para-) Contact Submanifolds Of Nearly(Para-) Kaehler Manifolds

This dissertation mainly study almost(para-)contact submanifolds of nearly(para-)Kaehler manifolds,which consists of six chapters.In the first chapter,we introduce an almost contact Lagrangian submanifold in the nearly Kaehler manifold S6,which is the promotion of the results of[37].We give conditions for which a canonically induced almost contact metric structure on the Lagrangian submanifold of L6 by a unit vector field,should be nearly Sasakian,(nearly)Kenmotsu,(nearly)cosymplectic and quasi-Sasakian.Furthermore,we conclude with a condition that reduces this normal canonically almost contact metric structure to Kenmotsu or cosymplectic structure.In the second chapter,we will discusses the almost contact hypersurface of neally Kaehler manifold S6.We provide conditions for which the almost contact metric structure on a real hypersurface of S6 should be Sasakian and nearly cosymplectic,and give an example of a real hypersurface in S6 to be Sasakian.In the third chapter,we will study the almost contact Lagrangian submanifold of nearly Kaehler manifold S3 × S3.We provide conditions for a canonically induced al-most contact metric structure on Lagralgian submanifold of S3×S3 by a unit vector field,to be a-Sasakian,β-Kenmotsu and cosymplectic.Furthermore,we conclude with a condition for which induced this normal canonically almost contact metric structure should be(?)-Sasakian or cosymplectic,(?)-Kenmotsu or cosymplectic s-turcture.In the fourth chapter,we just study the almost contact hypersurface of S3 × S3.We will provide conditions for which a real hypersurface of S3 × S3 should be(?)-Sasakian and cosymplectic under the special almost contact metric structure.In the fifth chapter,we initiate the study of the totally real submanifolds in near-ly para-Kaehler manifold H36.We will provide conditions for which a canonically induced almost para-contact metric structure on a 3-dimensional totally real sub-manifolds of H36 by a unit vector field,should be(nearly)para-Sasakian,(nearly)para-Kenmotsu and(nearly)para-cosymplectic.Furthermore,we conclude with a condition that reduces this normal canonically almost para-contact metric struc-ture to para-Sasakian or para-cosymplectic,para-Kenmotsu or para-cosymplectic structure.In the sixth chapter,we consider the hypersurface of nearly para-Kaehler manifold H36.We provide conditions for which the real hypersurface of H36 should be para-Sasakian and nearly para-cosymplectic under the special almost(para-)contact metric structures.