20 citations · 87 across the 22 of their papers we have counts for
22 papers
Biharmonic Hermitian vector bundles over compact Kaehlar Einstein manifolds
Hajime Urakawa
In this paper, we show that, for every Hermitian vector bundle over a compact Kaehler Einstein manifold, if the projection is biharmonic, then it is harmonic.
Harmonic morphisms of Allof-Wallach spaces of positive curvature
Hajime Urakawa
An infinite family of distinct harmonic morphisms with minimal circle fibers from the 7-dimensional homogeneous Allof-Wallach spaces of positive curvature onto the 6-dimensional fl…
Harmonic maps and biharmonic Riemanian submersions
Hajime Urakawa
Characterizations for Riemannian submersions to be harmonic or biharmonic are shown. Examples of biharmonic but not harmonic Riemannian submersions are shown.
Biharmonic homogeneous submanifolds in compact symmetric spaces and compact Lie groups
Shinji Ohno, Takashi Sakai, Hajime Urakawa
We give a necessary and sufficient condition for orbits of commutative Hermann actions and actions of the direct product of two symmetric subgroups on compact Lie groups to be biha…
Biharmonic homogeneous hypersurfaces in compact symmetric spaces
Shinji Ohno, Takashi Sakai, Hajime Urakawa
In this paper, we study biharmonic hypersurfaces in Einstein manifolds. Then, we determine all the biharmonic hypersurfaces in irreducible symmetric spaces of compact type which ar…
CR rigidity of pseudo harmonic maps and pseudo biharmonic maps
Hajime Urakawa
The CR analogue of B.-Y. Chen's conjecture on pseudo biharmonic maps will be shown. Pseudo biharmonic, but not pseudo harmonic, isometric immersions with parallel pseudo mean curva…
Biharmonic submanifolds in a Riemannian manifold
N. Koiso, H. Urakawa
In this paper, we solve affirmatively B.-Y. Chen's conjecture for hypersurfaces in the Euclidean space, under a generic condition. More precisely, every biharmonic hypersurface of…
The biharmonicity of sections of the tangent bundle
Michael Markellos, Hajime Urakawa
The bienergy of a vector field on a Riemannian manifold (M,g) is defined to be the bienergy of the corresponding map (M,g) ---> (TM,g_S), where the tangent bundle TM is equipped wi…
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…
Sasaki manifolds, Kaehler cone manifolds and biharmonic submanifolds
Hajime Urakawa
For a Legendrian submanifold of a Sasaki manifold , we study harmonicity and biharmonicity of the corresponding Lagrangian cone submanifold C(M) of a Kaehler manifold C(N).…
Conformal change of Riemannian metrics and biharmonic maps
Hisashi Naito, Hajime Urakawa
For the reduction ordinary differential equation due to Baird and Kamissoko \cite{BK} for biharmonic maps from a Riemannian manifold into another one , we show t…
Biharmonic Lagrangian submanifolds in Kähler manifolds
Shun Maeta, Hajime Urakawa
We give necessary and sufficient conditions for a Lagrangian submanifold of a Kähler manifold to be biharmonic. Furthermore, we classify biharmonic PNMC Lagrangian submanifolds in…
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 maps into symmetric spaces and integrable systems
Hajime Urakawa
In this paper, the description of biharmonic map equation in terms of the Maurer-Cartan form for all smooth map of a compact Riemannian manifold into a Riemannian symmetric space $…
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…
Projectively flat connections and flat connections on homogeneous spaces
Hajime Urakawa
We show a correspondence between the set of all G-invariant projectively flat connections on a homogeneous apace , and the one of all {G}^~-invariant flat connections on a h…
Classifications and Isolation Phenomena of Bi-Harmonic Maps and Bi-Yang-Mills Fields
Toshiyuki Ichiyama, Jun-ichi Inoguchi, Hajime Urakawa
Classifications of all biharmonic isoparametric hypersurfaces in the unit sphere, and all biharmonic homogeneous real hypersurfaces in the complex or quaternionic projective spaces…
Removable singularities and bubbling of harmonic maps and biharmonic maps
Nabumitsu Nakauchi, Hajime Urakawa
By using Moser's iteration technique, we show some removable singularity theorem of the tension field for biharmonic maps into manifolds of non-positive curvature, and the bubbling…
Biharmonic maps into compact Lie groups and the integrable systems
Hajime Urakawa
The reduction of biharmonic maps equation in terms of the Maurer-Cartan form for all smooth map of any compact Riemannian manifolds into a compact Lie group with bi-invariant Riema…
Yang-Mills fields on CR manifolds
Elisabetta Barletta, Sorin Dragomir, Hajime Urakawa
We study pseudo Yang-Mills fields on a compact strictly pseudoconvex CR manifold.