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121.
Indranil Biswas 《Geometriae Dedicata》2000,80(1-3):65-72
Given a compact connected oriented three manifold, equipped with a codimension one foliation, such that the Bott connection on the normal bundle is flat, a 2-form on the space parametrizing flat partial connections on it has been constructed. This form is closed. In the special case where the foliated three manifold is a surface bundle over the circle, this 2-form is identified with a certain 2-form on the parameter space for a class of paths in the representation space for the surface group. The 2-form, in question, on the parameter space for paths is constructed from the natural symplectic form on the representation space for a surface group. 相似文献
122.
ON THE CHERN CONNECTION OF FINSLER SUBMANIFOLDS 总被引:2,自引:0,他引:2
This paper studies the induced Chern connection of submanifolds in a Finsler manifold and gets the relations between the induced Chern connection and the Chern connection of the induced Finsler metric.Then the authors point out a difference between Finsler submanifolds and Riemann submanifolds. 相似文献
123.
射影半对称联络的一个不变量 总被引:1,自引:0,他引:1
本文研究与Levi-Civita联络▽射影等价地射影半对称联络D。获得了一个射影不变量,并给出其成立的一个充分必要条件。进而给出其保持相应共变导数不变的另一充分条件。 相似文献
124.
In this paper, we prove some inequalities between intrinsic and extrinsic curvature invariants, namely the normalized -Casorati curvatures and the scalar curvature of statistical submanifolds in Kenmotsu statistical manifolds of constant -sectional curvature that are endowed with semi-symmetric metric connection. Furthermore, we investigate the equality cases of these inequalities. We also describe an illustrative example. 相似文献
125.
126.
Increased urbanization has caused problems such as increasing water consumption and the continuous deterioration of the groundwater environment. It is necessary to consider the groundwater quality in the water resource optimization system and increase the rate of reclaimed water development to reduce the amount of groundwater exploitation and achieve sustainable development of water resources. This study used the Daxing District, a region of Beijing’s southern plain, as an example to evaluate water quality by analyzing water quality data of surface and groundwater from 2012 to 2016 and actual water-use schemes from 2006 to 2016. Three groundwater extraction modes were set up based on NO3–N concentrations, water resources were optimized under three extraction modes, and water resource optimization schemes were determined based on the improved connection entropy. The results show that (1) the surface water quality was poor, and the proportion of V4 type water in the indexes of NH3–N and chemical oxygen demand (COD) was the largest. The surface water can only be used for agricultural irrigation. The pollution sources contributing most to NH3–N and COD were domestic and agricultural pollution sources. (2) The groundwater quality was good. The NO3–N index was primarily type I–III water, accounting for 95.20% of the total samples. Severe NH3–N pollution areas were mainly in the northern region, and most regional groundwater can be used for various purposes. (3) Taking 2016 as an example, three groundwater exploitation modes were set to optimize water resource allocation, and the results showed that the rate of groundwater development and NO3–N pollution decreased significantly after optimization. (4) Connection entropy is an evaluation method that combines connection numbers and entropy, including identify, difference, and opposition entropy. As connection entropy being a kind of complete entropy, which can reflect the difference of the system in different states, based on the improved connection entropy, the connection entropies of optimal water resource allocation and actual water-use schemes were calculated. The connection entropy of groundwater exploitation mode 3 was less than that of groundwater exploitation modes 1 and 2 and actual water-use schemes from 2006 to 2016. Therefore, exploitation mode 3’s water resource optimization scheme was recommended. In the paper, satisfactory results have been obtained. As a kind of complete entropy, connection entropy has great research value in dealing with complex hydrological problems. This study’s research methods and outcomes can provide methodological and theoretical lessons for water management in freshwater-deficient areas. 相似文献
127.
We construct a formal connection on the Aomoto complex of an arrangement of hyperplanes, and use it to study the Gauss–Manin connection for the moduli space of the arrangement in the cohomology of a complex rank one local system. We prove that the eigenvalues of the Gauss–Manin connection are integral linear combinations of the weights which define the local system. 相似文献
128.
We study dually flat structures on symmetric cones associated with Jordan algebras. We give an interpretation of connections, a geometrical concept, in terms of Jordan algebras and show a relation between doubly autoparallel submanifolds and Jordan subalgebras. 相似文献
129.
Summary We consider a family ofq-dimensional (q>1), volume-preserving maps depending on a small parameterε. Asε → 0+ these maps asymptote to flows which attain a heteroclinic connection. We show that for smallε the heteroclinic connection breaks up and that the splitting between its components scales withε likeε
γexp[-β/ε]. We estimateβ using the singularities of theε → 0+ heteroclinic orbit in the complex plane. We then estimateγ using linearization about orbits in the complex plane. These estimates, as well as the assertions regarding the behavior
of the functions in the complex plane, are supported by our numerical calculations.
Deceased. 相似文献
130.
We construct a flat holomorphic line bundle over a connected component of the Hurwitz space of branched coverings of the Riemann
sphere P
1. A flat holomorphic connection defining the bundle is described in terms of the invariant Wirtinger projective connection
on the branched covering corresponding to a given meromorphic function on a Riemann surface of genus g. In genera 0 and 1 we construct a nowhere vanishing holomorphic horizontal section of this bundle (the ‘Wirtinger tau-function’).
In higher genus we compute the modulus square of the Wirtinger tau-function. In particular one gets formulas for the isomonodromic
tau-functions of semisimple Frobenius manifolds connected with the Hurwitz spaces H
g,N
(1,⋯,1).
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献