Displaying similar documents to “Isometric immersions of the hyperbolic space H n ( - 1 ) into H n + 1 ( - 1 )

On local isometric immersions into complex and quaternionic projective spaces

Hans Jakob Rivertz (2011)

Archivum Mathematicum

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We will prove that if an open subset of P n is isometrically immersed into P m , with m < ( 4 / 3 ) n - 2 / 3 , then the image is totally geodesic. We will also prove that if an open subset of P n isometrically immersed into P m , with m < ( 4 / 3 ) n - 5 / 6 , then the image is totally geodesic.

Normally flat semiparallel submanifolds in space forms as immersed semisymmetric Riemannian manifolds

Ülo Lumiste (2002)

Commentationes Mathematicae Universitatis Carolinae

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By means of the bundle of orthonormal frames adapted to the submanifold as in the title an explicit exposition is given for these submanifolds. Two theorems give a full description of the semisymmetric Riemannian manifolds which can be immersed as such submanifolds. A conjecture is verified for this case that among manifolds of conullity two only the planar type (in the sense of Kowalski) is possible.