Higher rank homogeneous Clifford structures
نویسندگان
چکیده
We give an upper bound for the rank r of homogeneous (even) Clifford structures on compact manifolds of non-vanishing Euler characteristic. More precisely, we show that if r = 2a · b with b odd, then r ≤ 9 for a = 0, r ≤ 10 for a = 1, r ≤ 12 for a = 2 and r ≤ 16 for a ≥ 3. Moreover, we describe the four limiting cases and show that there is exactly one solution in each case. 2010 Mathematics Subject Classification: Primary: 53C30, 53C35, 53C15. Secondary: 17B22
منابع مشابه
Homogeneous Clifford structures
We give an upper bound for the rank r of homogeneous (even) Clifford structures on compact manifolds of non-vanishing Euler characteristic. More precisely, we show that if r = 2 · b with b odd, then r ≤ 9 for a = 0, r ≤ 10 for a = 1, r ≤ 12 for a = 2 and r ≤ 16 for a ≥ 3. Moreover, we describe the four limiting cases and show that there is exactly one solution in each case. 2010 Mathematics Sub...
متن کاملCurves and Symmetric Spaces, II
We describe the canonical model of an algebraic curve of genus 9 over a perfect field when the Clifford index is maximal (=3) by means of linear systems of higher rank. Let SpG(n, 2n) be the symplectic Grassmannian, that is, the Grassmannian of Lagrangian subspaces of a 2n-dimensional symplectic vector space, over a field k. In the case n = 3, SpG(3, 6) is a 6-dimensional homogeneous variety an...
متن کاملA note on Clifford-Klein forms
We consider the problem of finding Clifford-Klein forms in a class of homogeneous spaces determined by inclusions of real Lie algebras of a special type which we call strongly regular. This class of inclusions is described in terms of their Satake diagrams. For example, the complexifications of such inclusions contain the class of subalgebras generated by automorphisms of finite order. We show ...
متن کاملClifford algebra unveils a surprising geomet- ric significance of quaternionic root systems of Coxeter groups
Quaternionic representations of Coxeter (reflection) groups of ranks 3 and 4, as well as those of E8, have been used extensively in the literature. The present paper analyses such Coxeter groups in the Clifford Geometric Algebra framework, which affords a simple way of performing reflections and rotations whilst exposing more clearly the underlying geometry. The Clifford approach shows that the...
متن کاملClifford Structures on Riemannian Manifolds
We introduce the notion of even Clifford structures on Riemannian manifolds, which for rank r = 2 and r = 3 reduce to almost Hermitian and quaternion-Hermitian structures respectively. We give the complete classification of manifolds carrying parallel rank r even Clifford structures: Kähler, quaternion-Kähler and Riemannian products of quaternion-Kähler manifolds for r = 2, 3 and 4 respectively...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. London Math. Society
دوره 87 شماره
صفحات -
تاریخ انتشار 2013