Submanifolds Of Nearly Para-K(?)hler Manifolds H₃⁶

Submanifold geometry is one of the most important contents in the study of differential geometry,among which nearly para-Kahler manifold is a very popular research object.In this paper,submanifolds with nearly para-Kahler structure in nearly para-Kahler manifold H36 will be studied in depth.This dissertation is divided into four chapters.The introduction part mainly introduces the research background and progress related to this thesis,and explains some of the research methods and research results of this thesis.The first chapter reviews some related definitions and symbols of the nearly para-Kahler manifold and some related knowledge of(almost)para-contact metric structures.Nearly para-Kahler structure on H36 is constructed and the relevant formulas and other important properties of the tensor field G on H36 are given.The second chapter mainly describes the necessary and sufficient conditions for a canonically induced almost para-contact metric structure by a unit vector field ? of a Lagrangian submanifolds M of the nearly para-Kahler manifolds H36.to be quasi-para-Sasakian,?-para-Kenmotsu.In addition,a tensor field h is defined on the induced para-contact metric,proving a property of tensor field h.At the same time,a necessary condition is derived when a canonically induced para-contact metric structure on M is para-Sasakian.The third chapter mainly considers the totally real surface on the nearly para-Kahler manifold H36.Firstly,it is proved that a complete totally real 2-dimensional surface of H36 is flat and minimal.Secondly,suppose that a minimal spacelike totally real surface M of H36 is homeomorphic to a sphere,For a₃,a₄,c,d,we have the following relationship(?)a₃=a₄=c=d=t1;(?)a₃=-a₄=-c=d=t₂;(?)a₃=-a₄=c=-d=t₃;(?)a₃=a₄=-c=-d=t₄;(?)-a₃=-a₄=c=d=t₅;(?)-a₃=a₄=-c=d=t₆;(?)-a₃=a₄-c=-d=t₇.If a₃=a₄=c=d=0,then M is totally geodesic.