Deformations of associative submanifolds with boundary
نویسندگان
چکیده
Let M be a compact smooth manifold of holonomy G2. We prove that the space of infinitesimal associative deformations of a compact associative submanifold Y with boundary in a coassociative submanifold X is the solution space of an elliptic problem. Further, we compute its virtual dimension. For ∂Y connected it is given by ∫ ∂Y c1(νX)+ 1− g, where g denotes the genus of ∂Y , νX the orthogonal complement of T∂Y in TX|∂Y and c1(νX) the first Chern class of νX with respect to its natural complex structure. MSC 2000: 53C38 (35J55, 53C29, 58J32).
منابع مشابه
Vanishing theorems for associative submanifolds
Let M7 a manifold with holonomy in G2, and Y 3 an associative submanifold with boundary in a coassociative submanifold. In [5], the authors proved that MX,Y , the moduli space of its associative deformations with boundary in the fixed X, has finite virtual dimension. Using Bochner’s technique, we give a vanishing theorem that forces MX,Y to be locally smooth. MSC 2000: 53C38 (35J55, 53C21, 58J32).
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