Real hypersurfaces which are contact in a nonflat complex space form
Let \(\widetilde{M^n}(c)\), \(n \geq 2\), be a complex \(n\)-dimensional complete and simply connected Kähler manifold of constant holomorphic sectional curvature \(c \neq 0.\) As is well-known, every real hypersurface \(M^{2n-1}\) of \(\widetilde{M^n}(c)\) admits an almost contact metric structure \((\phi, \xi,\nu, g)\) induced from this ambient space. The authors investigate real hypersurfaces in \(\widetilde{M^n}(c)\) whose induced structure \((\phi, \xi,\nu, g)\) is a contact metric structure linking in this way submanifold theory and contact geometry and show nice examples of contact manifolds from the viewpoint of submanifold theory. They show that every real hypersurface which is contact in \(\widetilde{M^n}(c)\) is an orbit of some subgroup of the isometry group \(I(\widetilde{M^n}(c))\) of the ambient space \(\widetilde{M^n}(c).\)
homogeneous real hypersurfaces of type (B)
scientific article; zbMATH DE number 5931182