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Shilnikov Lemma for a normally hyperbolic critical manifold of a Hamiltonian system
Shilnikov Lemma normally hyperbolic critical manifold Hamiltonian system
2015/3/18
Shilnikov Lemma for a normally hyperbolic critical manifold of a Hamiltonian system.
Geodesics and distance on the Riemannian manifold of Riemannian metrics
the Riemannian manifold Riemannian metrics
2010/11/11
Given a fixed closed manifold M, we exhibit an explicit formula for the distance function of the canonical L^2 Riemannian metric on the manifold of all smooth Riemannian metrics on M. Additionally, w...
Determining When The Universal Abelian Cover of a Graph Manifold is a Rationla Homology Sphere
Universal Abelian Cover Graph Rationla Homology Sphere
2010/11/8
It was shown in my earlier article that the splice diagram of a rational homology sphere graph manifold determines the manifolds universal abelian cover. In this article we use the proof of this to g...
The energy of a conformal warped manifold and applications
conformal warped manifold applications
2010/11/18
We introduce and study the notion of the energy of a conformally warped manifold, which includes as special cases the Yamabe constant and Perelman's $\nu$-entropy. We then investigate some properties...
Combined space-time manifold and the quantum geometry
Relativity quantum unification particle wave duality
2010/9/13
In a previous article we defined ”combined manifold” M3 as the graph of a diffeomorphism from one manifold M1 to another M2, akin to the idea of a diagonal map. In this paper, we derive the values for...
An affine embedding of the gamma manifold
gamma manifold statistical manifold affine immersion
2009/1/12
For the space of gamma distributions with Fisher metric and exponential connec-
tions, natural coordinate systems, potential functions and an affine immersion
in R3 are provided.
The model form and the \zeta-function for an elliptic differential operator of the second order on a manifold with turning points
model form turning manifold turning point
2010/9/10
This work represents the results of our research of the elliptic operator of the second order on a closed smooth manifold with the presence of turning points. The techniques, that were used in prevous...
An introduction of a combined space-time manifold
4-manifolds dark matter dual universe invisible energy
2010/9/15
This paper introduces the term, ”combined manifold,” which essentially is the graph of a diffeomorphism from one manifold to another.Following a previously published article about “invisible energies”...
Connections on Complex Finsler Manifold
complex Minkowski functional complex Finsler manifold
2007/12/11
We introduce Finsler metric on complex manifold and discuss connections induced by this metric.
Reduction of Volume-preserving Flows on an n-dimensional Manifold
non-autonomous lienard system periodic solution
2007/12/10
A geometric reduction procedure for volume-preserving flows with a volume-preserving symmetry on an n-dimensional manifold is obtained. Instead of the coordinate-dependent theory and the concrete coor...