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51.
K. D. Kirchberg has given a minoration of the absolute value of the eigenvalues of the Dirac operator for a compact Kähler spin manifold (W,g) with positive scalar curvature and has introduced, in this context, the notion of Kähler twistor-spinor. We prove here that if dimC W = p 4 is even, in the limiting case, (W, g) is the Kähler product of an odd-dimensional limiting case compact Kähler spin manifold of complex dimension (p-1), by a flat Kähler manifold which is a compact quotient of C. 相似文献
52.
S. Yu. Nemirovskii 《Mathematical Notes》1996,60(3):306-312
In the paper, we consider applications of strictly pseudoconvex domains to the problems of algebraicity and rationality. We
give a new proof of the Kodaira theorem on the algebraicity of a surface and we also prove a multidimensional version of this
theorem. Theorems analogous to the Hodge index theorem and the Lefschetz theorem about (1, 1)-classes are obtained for strictly
pseudoconvex domains. Conjectures on the geometry of strictly pseudoconvex domains on algebraic surfaces are formulated.
Translated fromMatematicheskie Zametki, Vol. 60, No. 3, pp. 414–422, September, 1996.
This research was supported by the Russian Foundation for Basic Research under grant No. 93-01-00225 and by the International
Science Foundation under grant No. 508. 相似文献
53.
ZHANG YongBing 《中国科学A辑(英文版)》2009,(8)
We use the contact Yamabe flow to find solutions of the contact Yamabe problem on K-contact manifolds. 相似文献
54.
55.
Taylan Şengül;Burhan Tiryakioglu;Esmanur Yıldız Akıl; 《Studies in Applied Mathematics》2024,153(3):e12735
In this study, the dynamics of a reaction–diffusion equation on a bounded interval at the first dynamic transition point is investigated. The main difference of this study from the existing ones in the dynamic transition literature is that in this work, no specific form of the nonlinear operator is assumed except that it is an analytic function of u$u$ and ux$u_x$. The linear operator is also assumed to be a general operator with sinusoidal eigenvectors. Moreover, we assume that there is a first transition as a real simple eigenvalue changes sign. With this general framework, we make a rigorous analysis of the dependence of the first transition dynamics on the coefficients of the Taylor expansion of the nonlinear operator. The main tool we use in this study is the center manifold reduction combined with the classification of the dynamic transition theory. This study is a generalization of a recent work where the nonlinear operator contains only low-order (quadratic and cubic) nonlinearities. The current generalization requires certain technical difficulties such as the validity of the genericity conditions on the Taylor coefficients of the nonlinear operator and a bootstrapping argument using these genericity conditions. The results of this work can be generalized in various directions, which are discussed in the conclusions section. 相似文献
59.
Geometry of affine immersions is the study of hypersurfaces that are invariant under affine transformations. As with the hypersurface theory on the Euclidean space, an affine immersion can induce a torsion-free affine connection and a (pseudo)-Riemannian metric on the hypersurface. Moreover, an affine immersion can induce a statistical manifold, which plays a central role in information geometry. Recently, a statistical manifold with a complex structure is actively studied since it connects information geometry and Kähler geometry. However, a holomorphic complex affine immersion cannot induce such a statistical manifold with a Kähler structure. In this paper, we introduce complex affine distributions, which are non-integrable generalizations of complex affine immersions. We then present the fundamental theorem for a complex affine distribution, and show that a complex affine distribution can induce a statistical manifold with a Kähler structure. 相似文献
60.