Title: Ricci tensors of real hypersurfaces in a complex projective space
Abstract: This paper gives a classification of real hypersurfaces in a complex projective space under assumptions that the structure vector <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="xi"> <mml:semantics> <mml:mi>ξ<!-- ξ --></mml:mi> <mml:annotation encoding="application/x-tex">\xi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is principal, the focal map has constant rank, and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="nabla Subscript xi Baseline upper S equals 0"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi mathvariant="normal">∇<!-- ∇ --></mml:mi> <mml:mi>ξ<!-- ξ --></mml:mi> </mml:msub> </mml:mrow> <mml:mi>S</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">{\nabla _\xi }S = 0</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, where <italic>S</italic> is the Ricci tensor of the real hypersurface.