By Proceedings of the International Workshop in Honor of S Maeda's 60th Birthday

This quantity is a compilation of papers offered on the convention on differential geometry, specifically, minimum surfaces, genuine hypersurfaces of a non-flat advanced house shape, submanifolds of symmetric areas and curve idea. It additionally includes new effects or short surveys in those parts. This quantity offers primary wisdom to readers (such as differential geometers) who're drawn to the speculation of actual hypersurfaces in a non-flat advanced area shape.

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**Example text**

1. The 1st equation in (11) is nothing but the condition that the Gaussian curvature of H13 is identically equal to −1. The 2nd and 3rd equations in (11) are respectively equivalent to the Codazzi equations hxx;y = hxy;x and hxy;y = hyy;x . We now assume that M is an oriented spacelike minimal surface in H13 . M is minimal if and only if hxx + hyy = 0, (12) September 4, 2013 36 17:10 WSPC - Proceedings Trim Size: 9in x 6in main T. Ichiyama & S. Udagawa which gives hxx hyy − (hxy )2 = − (hxx )2 + (hxy )2 .

For γ = 0 and γ = 1, Meeks’ M¨obius strip [10] and L´opez’ Klein bottle [9] satisfy deg(g) = γ + 3, respectively. But, for γ ≥ 2, no examples with deg(g) = γ + 3 are known. So, it is interesting to give a minimal surface satisfying deg(g) = γ + 3 with an antiholomorphic involution without fixed points. References 1. C. C. Chen and F. Gackstatter, Elliptische und hyperelliptische Funktionen und vollstandige Minimalflachen vom Enneperschen Typ, Math. Ann. 259 (1982), 359-369. 2. A. Costa, Examples of a Complete Minimal Immersion in of Genus One and Three Embedded Ends, Bil.

179 (1982), 337–344. 38. S. Maeda and H. Tanabe, Totally geodesic immersions of K¨ ahler manifolds and K¨ ahler Frenet curves, Math. Z. 252 (2006), 787–795. 39. S. Maeda and K. Tsukada, Isotropic immersions into a real space form, Canad. Math. Bull. 37 (1994), 245–253. 40. S. Maeda and S. Udagawa, Characterization of parallel isometric immersions of space forms into space forms in the class of isotropic immersions, Canadian J. Math. 61 (2009), 641-655. Received August 7, 2012. jp Dedicated to Professor Sadahiro Maeda on his 60th birthday We have shown [3] that if the projective developing map of a regular curve in the sphere is injective then the curve has no self-intersection.