Biharmonic submanifolds in manifolds with bounded curvature
Maeta, Shun
Original · EN
We consider a complete biharmonic submanifold ϕ:(M,g)→ (N,h) in a Riemannian manifold with sectional curvature bounded from above by a non-negative constant c. Assume that the mean curvature is bounded from below by √ c. If (i) ∫ₘ (| H|²-c)ᵖdvg<∞, for some 0<p<∞, or (ii) the Ricci curvature of M is bounded from below, then the mean curvature is √ c. Furthermore, if M is compact, then we obtain the same result without the assumption (i) or (ii).
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