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6 papers · 1 filter
On the index of constant mean curvature 1 surfaces in hyperbolic space
Levi Lopes de Lima, Wayne Rossman
We show that the index of a constant mean curvature 1 surface in hyperbolic 3-space is completely determined by the compact Riemann surface and secondary Gauss map that represent i…
A representation formula for indefinite improper affine spheres
Daisuke Nakajo
We construct a new representation formula for indefinite improper affine spheres in terms of two para-holomorphic functions and study singularities which appear in this representat…
Behavior of corank one singular points on wave fronts
Kentaro Saji, Masaaki Umehara, Kotaro Yamada
Let be an oriented 2-manifold and a -map. A point is called a singular point if is not an immersion at . The map is called a fr…
Uniqueness and examples of compact toric Sasaki-Einstein metrics
Koji Cho, Akito Futaki, Hajime Ono
In [11] it was proved that, given a compact toric Sasaki manifold of positive basic first Chern class and trivial first Chern class of the contact bundle, one can find a deformed S…
The geometry of fronts
Kentaro Saji, Masaaki Umehara, Kotaro Yamada
We shall introduce the singular curvature function on cuspidal edges of surfaces, which is related to the Gauss-Bonnet formula and which characterizes the shape of cuspidal edges.…
Flat fronts in hyperbolic 3-space
Masatoshi Kokubu, Masaaki Umehara, Kotaro Yamada
We shall investigate flat surfaces in hyperbolic 3-space with admissible singularities, called `flat fronts'. An Osserman-type inequality for complete flat fronts is shown. When eq…