The author establishes in this paper the following results: (1) In a quasiconstant curvature manifold M a parallel tensor of type is constant multiple of the metric tensor. (2) On a quasi_constant curvature manifold ...The author establishes in this paper the following results: (1) In a quasiconstant curvature manifold M a parallel tensor of type is constant multiple of the metric tensor. (2) On a quasi_constant curvature manifold there is no nonzero parallel 2_form. Unless the Ricci principal curvature corresponding to the generator of M is equal to zero.展开更多
In this paper, by using the method of tensor operation, the fundamental solutions, given in the references listed, for a concentrated force in a three-dimensional biphase-infinite solid were expressed in the tensor fo...In this paper, by using the method of tensor operation, the fundamental solutions, given in the references listed, for a concentrated force in a three-dimensional biphase-infinite solid were expressed in the tensor form, which enables them to be directly applied to the boundary integral equation and the boundary element method for solving elastic mechanics problems of the bimaterial space. The fundamental solutions for Mindlin's problem, Lorentz's problem and homogeneous space problem are involved in the present results.展开更多
In this article we study the two-dimensional completeλ-translators immersed in the Euclidean space R^3 and Minkovski space R1^ 3.We obtain two classification theorems:one for two-dimensional completeλ-translators x:...In this article we study the two-dimensional completeλ-translators immersed in the Euclidean space R^3 and Minkovski space R1^ 3.We obtain two classification theorems:one for two-dimensional completeλ-translators x:M 2→R^3 and one for two-dimensional complete space-likeλ-translators x:M 2→R1^3,with a second fundamental form of constant length.展开更多
In the general theory of relativity, the fundamental metric tensor plays a special role, which has its physical basis in the peculiar aspects of gravitation. The fundamental property of gravitational fields provides t...In the general theory of relativity, the fundamental metric tensor plays a special role, which has its physical basis in the peculiar aspects of gravitation. The fundamental property of gravitational fields provides the possibility of establishing an analogy between the motion in a gravitational field and the motion in any external field considered as a noninertial system of reference. Thus, the properties of the motion in a noninertial frame are the same as those in an inertial system in the presence of a gravitational field. In other words, a noninertial frame of reference is equivalent to a certain gravitational field. This is known as the principle of equivalence. From the mathematical viewpoint, the same special role can be played by the small deformation strain tensor, which describes the geometrical properties of any region deformed because of the effect of some external agent. It can be proved that, from that tensor, all the mathematical structures needed in the general theory of relativity can be constructed.展开更多
Understanding of the basic properties of the positive semi-definite tensor is a prerequisite for its extensive applications in theoretical and practical fields, especially for its square-root. Uniqueness of the square...Understanding of the basic properties of the positive semi-definite tensor is a prerequisite for its extensive applications in theoretical and practical fields, especially for its square-root. Uniqueness of the square-root of a positive semi-definite tensor is proven in this paper without resorting to the notion of eigenvalues, eigenvectors and the spectral decomposition of the second-order symmetric tensor.展开更多
文摘The author establishes in this paper the following results: (1) In a quasiconstant curvature manifold M a parallel tensor of type is constant multiple of the metric tensor. (2) On a quasi_constant curvature manifold there is no nonzero parallel 2_form. Unless the Ricci principal curvature corresponding to the generator of M is equal to zero.
文摘In this paper, by using the method of tensor operation, the fundamental solutions, given in the references listed, for a concentrated force in a three-dimensional biphase-infinite solid were expressed in the tensor form, which enables them to be directly applied to the boundary integral equation and the boundary element method for solving elastic mechanics problems of the bimaterial space. The fundamental solutions for Mindlin's problem, Lorentz's problem and homogeneous space problem are involved in the present results.
基金Foundation of Natural Sciences of China(11671121,11871197 and 11971153)。
文摘In this article we study the two-dimensional completeλ-translators immersed in the Euclidean space R^3 and Minkovski space R1^ 3.We obtain two classification theorems:one for two-dimensional completeλ-translators x:M 2→R^3 and one for two-dimensional complete space-likeλ-translators x:M 2→R1^3,with a second fundamental form of constant length.
文摘In the general theory of relativity, the fundamental metric tensor plays a special role, which has its physical basis in the peculiar aspects of gravitation. The fundamental property of gravitational fields provides the possibility of establishing an analogy between the motion in a gravitational field and the motion in any external field considered as a noninertial system of reference. Thus, the properties of the motion in a noninertial frame are the same as those in an inertial system in the presence of a gravitational field. In other words, a noninertial frame of reference is equivalent to a certain gravitational field. This is known as the principle of equivalence. From the mathematical viewpoint, the same special role can be played by the small deformation strain tensor, which describes the geometrical properties of any region deformed because of the effect of some external agent. It can be proved that, from that tensor, all the mathematical structures needed in the general theory of relativity can be constructed.
文摘Understanding of the basic properties of the positive semi-definite tensor is a prerequisite for its extensive applications in theoretical and practical fields, especially for its square-root. Uniqueness of the square-root of a positive semi-definite tensor is proven in this paper without resorting to the notion of eigenvalues, eigenvectors and the spectral decomposition of the second-order symmetric tensor.
