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138
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 25 (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 (14 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.
Natural and projectively equivariant quantizations by means of Cartan connections
 Lett. Math. Phys
, 2005
"... Abstract. The existence of a natural and projectively equivariant quantization in the sense of Lecomte [20] was proved recently by M. Bordemann [4], using the framework of ThomasWhitehead connections. We give a new proof of existence using the notion of Cartan projective connections and we obtain a ..."
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Cited by 17 (9 self)
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Abstract. The existence of a natural and projectively equivariant quantization in the sense of Lecomte [20] was proved recently by M. Bordemann [4], using the framework of ThomasWhitehead connections. We give a new proof of existence using the notion of Cartan projective connections and we obtain an explicit formula in terms of these connections. Our method yields the existence of a projectively equivariant quantization if and only if an sl(m + 1, R)equivariant quantization exists in the flat situation in the sense of [18], thus solving one of the problems left open by M. Bordemann.
Holonomy reductions of Cartan geometries and curved orbit decompositions
, 2011
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Branching laws for Verma modules and applications in parabolic geometry
"... We initiate a new study of differential operators with symmetries and combine this with the study of branching laws for Verma modules of reductive Lie algebras. By the criterion for discretely decomposable and multiplicityfree restrictions of generalized Verma modules [T. Kobayashi, Transf. Groups ..."
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Cited by 15 (7 self)
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We initiate a new study of differential operators with symmetries and combine this with the study of branching laws for Verma modules of reductive Lie algebras. By the criterion for discretely decomposable and multiplicityfree restrictions of generalized Verma modules [T. Kobayashi, Transf. Groups (2012)], we are brought to natural settings of parabolic geometries for which there exist unique equivariant differential operators to submanifolds. Then we apply a new method (Fmethod) relying on the Fourier transform to find singular vectors in generalized Verma modules, which significantly simplifies and generalizes many preceding works. In certain cases, it also determines the Jordan–Hölder series of the restriction for singular parameters. The Fmethod yields an explicit formula of such unique operators, for example, giving an intrinsic and new proof of Juhl’s conformally invariant differential operators [Juhl, Progr. Math. 2009] and its generalizations to spinor bundles. This article is the first in the series, and the next ones include their extension to curved cases together with more applications of the Fmethod to various settings in parabolic geometries.
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 12 (9 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