7 citations · 13 across the 3 of their papers we have counts for
6 papers · 1 filter
Triharmonic isometric immersions into a manifold of non-positively constant curvature
Shun Maeta, Nobumitsu Nakauchi, Hajime Urakawa
A triharmonic map is a critical point of the 3-energy in the space of smooth maps between two Riemannian manifolds. We study a triharmonic isometric immersion into a space form of…
Polyharmonic maps into the Euclidean space
Nobumitsu Nakauchi, Hajime Urakawa
We study polyharmonic (k-harmonic) maps between Riemannian manifolds with finite j-energies (j=1, cdots, 2k-2). We show if the domain is complete and the target is the Euclidean sp…
Weak conformality of stable stationary maps for a functional related to conformality
Shigeo Kawai, Nobumitsu Nakauchi
Let , be compact Riemannian manifolds without boundary, and let be a smooth map from into . We consider a covariant symmetric tensor ${\displa…
Biharmonic submanifolds in a Riemannian manifold with non-positive curvature
Nobumitsu Nakauchi, Hajime Urakawa
We show that for an isometric immersion of a complete Riemannian manifold into a Riemannian manifold with non-positive curvature, the norm of the mean curvature vector field is squ…
Biharmonic maps into a Riemannian manifold of non-positive curvature
Nobumitsu Nakauchi, Hajime Urakawa, Sigmundur Gudmundsson
We study biharmonic maps between Riemannian manifolds with finite energy and finite bi-energy. We show that if the domain is complete and the target of non-positive curvature, then…
Biharmonic hypersurfaces in a Riemannian manifold with non-positive Ricci curvature
Nobumitsu Nakauchi, Hajime Urakawa
In this paper, we show that, for a biharmonic hypersurface of a Riemannian manifold of non-positive Ricci curvature, if , where is the m…