Geodesic Laminations with Closed Ends on Surfaces and Morse Index; Kupka-smale Metrics
نویسنده
چکیده
γ uLγ u where Lγ u = u ′′ +K u, the Morse index is the number of negative eigenvalues of Lγ. (By convention, an eigenfunction φ with eigenvalue λ of Lγ is a solution of Lγ φ+ λφ = 0.) Note that if λ = 0, then φ (or φn) is a (normal) Jacobi field. γ is stable if the index is zero. The index of a noncompact geodesic is the dimension of a maximal vector space of compactly supported variations for which the second derivative of length is negative definite. We also say that such a geodesic is stable if the index is 0.
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تاریخ انتشار 2008