Differential Geometry of Submanifolds and Its Related Topics by Proceedings of the International Workshop in Honor of S

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

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

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Example text

In fact, Meeks [10] showed that the Euler characteristic χ(M γ ) and 2 deg(g) are congruent modulo 4, where g is the Gauss map of f . By these facts, we can observe that for every complete non-orientable minimal surface of finite total curvature, deg(g) ≥ γ + 3 holds. 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.

16. T. Adachi, S. Maeda and S. Udagawa, Circles in a complex projective space, Osaka J. Math. 32 (1995), 709–719. 17. T. Adachi, S. Maeda and S. Udagawa, Ruled real hypersurfaces in a nonflat quaternionic space form, Monatshefte Math. 145 (2005), 179–190. 18. T. Adachi, S. Maeda and S. Udagawa, Schur’s lemma for K¨ ahler manifolds, Arch. Math. (Basel) 90 (2008), 163–172. 19. T. Adachi, S. Maeda and M. Yamagishi, Length spectrum of geodesic spheres in a non-flat complex space form, J. Math. Soc.

We call them K¨ ahler magnetic fields (cf. [1, 6]).

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