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Toru Sasahara

Publications and source records attributed to Toru Sasahara.

16 recordsLinked to original sources
arXiv2026

Hamiltonian stationary Lagrangian surfaces in complex space forms with constant-length gradient of the mean curvature

We study Hamiltonian stationary Lagrangian surfaces in complex space forms with nowhere-zero mean curvature vector $H$. We prove that if the Gaussian curvature is constant and $\grad|H|$ has positive constant length, then both the surface and the ambient space are flat. Moreover, the immersion is locally congruent to the known surface obtained as the product of a Cornu spiral and its reflection.

math.DG↗
arXiv2026

Hamiltonian stationary Lagrangian surfaces with harmonic mean curvature in complex space forms

In this paper, we study Hamiltonian stationary Lagrangian surfaces in complex space forms. We first show that when the mean curvature is a non-zero constant, the second fundamental form is parallel. We then consider the case in which the mean curvature is a non-constant harmonic function. Under the additional assumption that the Gaussian curvature is constant, we obtain a complete classification of such Lagrangian surfaces.

math.DG↗
arXiv2023

Tangentially biharmonic Lagrangian H-umbilical submanifolds in complex space forms

The notion of Lagrangian $H$-umbilical submanifolds was introduced by B. Y. Chen in 1997, and these submanifolds have appeared in several important problems in the study of Lagrangian submanifolds from the Riemannian geometric point of view. Recently, the author introduced the notion of tangentially biharmonic submanifolds, which are defined as submanifolds such that the bitension field of the inclusion map has vanishing tangential component. The normal bundle of a round hypersphere in $\mathbb{R}^n$ can be immersed as a tangentially biharmonic Lagrangian $H$-umbilical submanifold in $\mathbb{C}^n$. Motivated by this fact, we classify tangentially biharmonic Lagrangian $H$-umbilical submanifolds in complex space forms.

math.DG↗
arXiv2022

Special slant surfaces with non-constant mean curvature in 2-dimensional complex space forms

In the late 1990s, B. Y. Chen introduced the notion of special slant surfaces in Kähler surfaces and classified non-minimal proper special slant surfaces with constant mean curvature in $2$-dimensional complex space forms. In this paper, we completely classify proper special slant surfaces with non-constant mean curvature in $2$-dimensional complex space forms.

math.DG↗
arXiv2021

Real hypersurfaces in the complex projective plane satisfying an equality involving $δ(2)$

It was proved in Chen's paper \cite{chen} that every real hypersurface in the complex projective plane of constant holomorphic sectional curvature $4$ satisfies $$ δ(2)\leq \frac{9}{4}H^2+5,$$ where $H$ is the mean curvature and $δ(2)$ is a $δ$-invariant introduced by him. In this paper, we study non-Hopf real hypersurfaces satisfying the equality case of the inequality under the condition that the mean curvature is constant along each integral curve of the Reeb vector field. We describe how to obtain all such hypersurfaces.

math.DG↗
arXiv2018

Ricci curvature of real hypersurfaces in non-flat complex space forms

We establish an inequality among the Ricci curvature, the squared mean curvature, and the normal curvature for real hypersurfaces in complex space forms. We classify real hypersurfaces in two-dimensional non-flat complex space forms which admit a unit vector field satisfying identically the equality case of the inequality.

math.DG↗
arXiv2015

A short note on biharmonic submanifolds in non-Sasakian contact metric 3-manifolds

We characterize biharmonic anti-invariant surfaces in $3$-dimensional generalized $(κ, μ)$-manifolds with non-zero constant mean curvature by means of the scalar curvature of the ambient space and the mean curvature. In addition, we give a method for constructing infinity many examples of biharmonic submanifolds in a certain $3$-dimensional generalized $(κ, μ)$-manifold. Moreover, we determine $3$-dimensional generalized $(κ, μ)$-manifolds which admit a certain kind of proper biharmonic foliation.

math.DG↗
arXiv2015

A short survey on $δ$-ideal CR submanifolds

This paper surveys some of the known results on $δ$-ideal CR submanifolds in complex space forms, the nearly Kähler $6$-sphere and odd dimensional unit spheres. In addition, the relationship between $δ$-ideal CR submanifolds and critical points of the $λ$-bienergy is mentioned. Some topics on variational problem for the $λ$-bienergy are also presented.

math.DG↗
arXiv2014

Surfaces in Euclidean 3-space whose normal bundles are tangentially biharmonic

A submanifold is said to be tangentially biharmonic if the bitension field of the isometric immersion that defines the submanifold has vanishing tangential component. The purpose of this paper is to prove that a surface in Euclidean $3$-space has tangentially biharmonic normal bundle if and only if it is either minimal, a part of a round sphere, or a part of a circular cylinder.

math.DG↗