Presentation Title

P-36 An inequality on Riemannian submersion invariant and theta-slant isometric immersion

Presenter Status

Department of Mathematics

Location

Buller Hallway

Start Date

1-11-2013 1:30 PM

End Date

1-11-2013 3:00 PM

Presentation Abstract

It has been known that if a Riemannian manifold admits a non-trivial Riemannian submersion with totally geodesic fibers, then it cannot be isometrically immersed in any Riemannian manifold of non-positive sectional curvature as a minimal submanifold. B.Y. Chen proved this using an inequality involving the submersion invariant and his inequality shows the upper bound of the invariant Ăπ if a manifold is Lagrangian submanifold. Recently, the lower bound was found and furthermore, another inequality can be derived if we consider a θ-slant submanifold in complex space forms.

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Nov 1st, 1:30 PM Nov 1st, 3:00 PM

P-36 An inequality on Riemannian submersion invariant and theta-slant isometric immersion

Buller Hallway

It has been known that if a Riemannian manifold admits a non-trivial Riemannian submersion with totally geodesic fibers, then it cannot be isometrically immersed in any Riemannian manifold of non-positive sectional curvature as a minimal submanifold. B.Y. Chen proved this using an inequality involving the submersion invariant and his inequality shows the upper bound of the invariant Ăπ if a manifold is Lagrangian submanifold. Recently, the lower bound was found and furthermore, another inequality can be derived if we consider a θ-slant submanifold in complex space forms.