In this note we present various extensions of Obata’s rigidity theorem concerning the Hessian of a function on a Riemannian manifold.They include general rigidity theorems for the generalized Obata equation,and hyper...In this note we present various extensions of Obata’s rigidity theorem concerning the Hessian of a function on a Riemannian manifold.They include general rigidity theorems for the generalized Obata equation,and hyperbolic and Euclidean analogs of Obata’s theorem.Besides analyzing the full rigidity case,we also characterize the geometry and topology of the underlying manifold in more general situations.展开更多
1922年日本学者小畑薰良翻译的《李白诗集》(The Works of Li Po:the Chinese Poet)在美国出版。该诗集是世界上第一部李白诗歌英译文集,在多方面呈现创新特性,并在西方世界产生长久的影响。考察该诗集的注释,可以发现,译者在注释时表...1922年日本学者小畑薰良翻译的《李白诗集》(The Works of Li Po:the Chinese Poet)在美国出版。该诗集是世界上第一部李白诗歌英译文集,在多方面呈现创新特性,并在西方世界产生长久的影响。考察该诗集的注释,可以发现,译者在注释时表义力求简洁、释义注重通约、优先择取趣味性信息和直接挑明暗示性信息。该诗集的注释原则为中国古代诗歌外译提供有益的启示。展开更多
In this paper, we derive an elementary identity for smooth solutions of the following equation:$$\Delta u\left( x \right) + K\left( x \right)e^{2u\left( x \right)} = 0\,{\rm in}\,R^2 $$and use it to get some global pr...In this paper, we derive an elementary identity for smooth solutions of the following equation:$$\Delta u\left( x \right) + K\left( x \right)e^{2u\left( x \right)} = 0\,{\rm in}\,R^2 $$and use it to get some global properties of the solutions.展开更多
文摘In this note we present various extensions of Obata’s rigidity theorem concerning the Hessian of a function on a Riemannian manifold.They include general rigidity theorems for the generalized Obata equation,and hyperbolic and Euclidean analogs of Obata’s theorem.Besides analyzing the full rigidity case,we also characterize the geometry and topology of the underlying manifold in more general situations.
文摘1922年日本学者小畑薰良翻译的《李白诗集》(The Works of Li Po:the Chinese Poet)在美国出版。该诗集是世界上第一部李白诗歌英译文集,在多方面呈现创新特性,并在西方世界产生长久的影响。考察该诗集的注释,可以发现,译者在注释时表义力求简洁、释义注重通约、优先择取趣味性信息和直接挑明暗示性信息。该诗集的注释原则为中国古代诗歌外译提供有益的启示。
文摘In this paper, we derive an elementary identity for smooth solutions of the following equation:$$\Delta u\left( x \right) + K\left( x \right)e^{2u\left( x \right)} = 0\,{\rm in}\,R^2 $$and use it to get some global properties of the solutions.
