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132
Remarks on the FrölicherNijenhuis bracket
 Proceedings of the Conference on Differential Geometry and its Applications
, 1986
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Bisimulation Relations for Dynamical and Control Systems
, 2002
"... In this paper we propose a new equivalence relation for dynamical and control systems called bisimulation. As the name implies this definition is inspired by the fundamental notion of bisimulation introduced by R. Milner for labeled transition systems. It is however, more subtle than its namesake in ..."
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Cited by 24 (9 self)
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In this paper we propose a new equivalence relation for dynamical and control systems called bisimulation. As the name implies this definition is inspired by the fundamental notion of bisimulation introduced by R. Milner for labeled transition systems. It is however, more subtle than its namesake in concurrency theory, mainly due to the fact that here, one deals with relations on manifolds. We further show that the bisimulation relations for dynamical and control systems defined in this paper are captured by the notion of abstract bisimulation of Joyal, Nielsen and Winskel (JNW). This result not only shows that our equivalence notion is on the right track, but also confirms that the abstract bisimulation of JNW is general enough to capture equivalence notions in the domain of continuous systems. We believe that the unification of the bisimulation relation for labeled transition systems and dynamical systems under the umbrella of abstract bisimulation, as achieved in this work, is a first step towards a unified approach to modeling of and reasoning about the dynamics of discrete and continuous structures in computer science and control theory.
SOBOLEV METRICS ON SHAPE SPACE OF SURFACES
"... Abstract. Let M and N be connected manifolds without boundary with dim(M) < dim(N), and let M compact. Then shape space in this work is either the manifold of submanifolds of N that are diffeomorphic to M, or the orbifold of unparametrized immersions of M in N. We investigate the Sobolev Riemanni ..."
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Cited by 21 (15 self)
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Abstract. Let M and N be connected manifolds without boundary with dim(M) < dim(N), and let M compact. Then shape space in this work is either the manifold of submanifolds of N that are diffeomorphic to M, or the orbifold of unparametrized immersions of M in N. We investigate the Sobolev Riemannian metrics on shape space: These are induced by metrics of the following form on the space of immersions:
Lifting smooth curves over invariants for representations of compact Lie groups
 TRANSFORMATION GROUPS
, 2000
"... We show that one can lift locally real analytic curves from the orbit space of a compact Lie group representation, and that one can lift smooth curves even globally, but under an assumption. ..."
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Cited by 19 (13 self)
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We show that one can lift locally real analytic curves from the orbit space of a compact Lie group representation, and that one can lift smooth curves even globally, but under an assumption.
Holonomy reductions of Cartan geometries and curved orbit decompositions
, 2011
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CURVATURE WEIGHTED METRICS ON SHAPE SPACE OF HYPERSURFACES IN nSPACE
"... Abstract. Let M be a compact connected oriented n−1 dimensional manifold without boundary. In this work, shape space is the orbifold of unparametrized immersions from M to Rn. The results of [1], where mean curvature weighted metrics were studied, suggest to incorporate Gauß curvature weights in the ..."
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Cited by 13 (10 self)
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Abstract. Let M be a compact connected oriented n−1 dimensional manifold without boundary. In this work, shape space is the orbifold of unparametrized immersions from M to Rn. The results of [1], where mean curvature weighted metrics were studied, suggest to incorporate Gauß curvature weights in the definition of the metric. This leads us to study metrics on shape space that are induced by metrics on the space of immersions of the form Gf (h, k) = Φ.¯g(h, k) vol(f
POISSON STRUCTURES ON DOUBLE LIE GROUPS
, 1997
"... Lie bialgebra structures are reviewed and investigated in terms of the double Lie algebra, of Manin and Gaußdecompositions. The standard Rmatrix in a Manin decomposition then gives rise to several Poisson structures on the correponding double group, which is investigated in great detail. ..."
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Cited by 12 (4 self)
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Lie bialgebra structures are reviewed and investigated in terms of the double Lie algebra, of Manin and Gaußdecompositions. The standard Rmatrix in a Manin decomposition then gives rise to several Poisson structures on the correponding double group, which is investigated in great detail.
structures on the cotangent bundle of a Lie group or a principle bundle and their reductions
 J. Math. Physics
, 1994
"... 1. Liouville 1forms on fiber bundles and the lifting of vector fields..... 3 2. The canonical Poisson structure on T ∗ G............... 5 3. Generalizing momentum mappings.................. 11 ..."
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Cited by 8 (8 self)
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1. Liouville 1forms on fiber bundles and the lifting of vector fields..... 3 2. The canonical Poisson structure on T ∗ G............... 5 3. Generalizing momentum mappings.................. 11
On The Geometry Of Almost Hermitian Symmetric Structures
"... The almost Hermitian symmetric structures include several important geometries, e.g. the conformal, projective, quaternionic or almost Grassmannian ones. The conformal case is known best and several efficient techniques have been worked out in the last 90 years. The present note provides links of t ..."
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Cited by 8 (3 self)
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The almost Hermitian symmetric structures include several important geometries, e.g. the conformal, projective, quaternionic or almost Grassmannian ones. The conformal case is known best and several efficient techniques have been worked out in the last 90 years. The present note provides links of the development presented in [CSS1, CSS2, CSS3, CSS4] to several other approaches and it suggests extensions of some techniques to all geometries in question.