NAGATOMO Yasuyuki    Department   Undergraduate School  , School of Science and Technology    Position   Professor
Research Period	2002～2005
Research Topic	Generalizations of Weierstrass-type representation formulae and applications
Research Type	KAKENHI Research
Consignor	Japan Society for the Promotion of Science
Research Program Type	Grant-in-Aid for Scientific Research (B)
KAKENHI Grant No.	14340024
Keyword	cuspidal edge, cuspidal cross cap, Weierstrass representation, singularities, front, flat surface, maximal surface, swallowtail
Responsibility	Research Contributor
Representative Person	YAMADA Kotaro
Details	1.W rewrote the Weierstrass-type representation formula for flat surfaces in hyperbolic 3-space in the form without integration (Darboux-type formula), and classified complete flat surfaces with small numbers of ends. 2.We pointed out the class of ambient spaces for which an analogue of Weierstrass-type (Bryant) representation formula for mean curvature one surfaces in hyperbolic 3-space holds. 3.We found criteria for singularities (cuspidal edges, swallowtails, cuspidal cross caps) which are generic singularities of fronts or frontals. 4.We established fundamental notions of flat fronts in hyperbolic 3-space, and investiagted properties of singularities of such surfaces. 5.We defined a certain class of maximal surfaces with singularities in Minkowski 3-space (called maxface), and investigated their singularities.