On real local isometric immersions of {\mathbb{C}Q^2_c} into {\mathbb{C} P^{3}} |
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Authors: | Hans Jakob Rivertz |
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Institution: | 1. The Faculty of Informatics and e-Learning, S?r-Tr?ndelag University College, 7004, Trondheim, Norway
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Abstract: | We investigate real local isometric immersions of Kähler manifolds ${\mathbb{C}Q^2_c}$ of constant holomorphic curvature 4c into complex projective 3-space. Our main result is that the standard embedding of ${\mathbb{C}P^2}$ into ${\mathbb{C}P^3}$ has strong rigidity under the class of local isometric transformations. We also prove that there are no local isometric immersions of ${\mathbb{C}Q^2_c}$ into ${\mathbb{C}P^3}$ when they have different holomorphic curvature. An important method used is a study of the relationship between the complex structure of any locally isometric immersed ${\mathbb{C}Q^2_c}$ and the complex structure of the ambient space ${\mathbb{C}P^3}$ . |
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