17,545 research outputs found

    Curvature-adapted submanifolds of symmetric spaces

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    We study curvature-adapted submanifolds of general symmetric spaces. We generalize Cartan's theorem for isoparametric hypersurfaces of spheres and Wang's classification of isoparametric Hopf hypersurfaces in complex projective spaces to any compact symmetric space. Our second objective is to investigate such hypersurfaces in some specific symmetric spaces. Various classification results in the Cayley projective and hyperbolic planes and in complex two-plane Grassmannians are obtained under some additional assumptions.Comment: Theorem 1.4 strengthened from previous version. To appear in Indiana. U. Math.

    On the linear stability of K\"ahler-Ricci solitons

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    This is a short note proving that K\"ahler-Ricci solitons with dimH(1,1)(M)2\dim H^{(1,1)}(M)\ge 2 are linearly unstable. This extends the results of Cao-Hamilton-Ilmanen in the K\"ahler-Einstein case.Comment: 11 pages; typos corrected, presentation improved and references added in v.

    Articulating Roles and Responsibilities in the Transition Planning Process: A Practice Aimed at Figuring Out How to Work Together

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    It is clear that the intention of the Individual with Disabilities Education Act require both the Education Agency and the Vocational Rehabilitation Agency (VESID, in New York State) to jointly participate in the development of transition plans for students with disabilities as they prepare for employment after high school. Yet, we find certain barriers to school and vocational rehabilitation (VR) collaboration, such as: poor or inaccurate perceptions of vocational rehabilitation; and conversely of schools and youth in transition by VR staff; as well as nonexistent or ineffective procedures to support collaboration between district and VR staff. This brief will highlight specific steps and strategies designed and implemented by a regional workgroup to remedy these barriers. Transition Articulation Agreements has improved procedures and communication among the partners. This brief will review the specific barriers faced, and interventions taken to remove barriers and create measures of success