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= Seeley-DeWitt coefficients=

= δ-invariants =

In Riemannian geometry, δ-invariants or Chen invariants, after Bang-Yen Chen, are a type of intrinsic geometric invariants of a Riemannian manifold.

Definition
Let $$M$$ be a d-dimensional Riemannian manifold, $$K(\pi)$$ the sectional curvature associated with a plane section $$\pi$$ of the tangent space $$T_pM$$ at a point $$p \in M$$, $$e_1, \ldots, e_d$$ an orthonormal basis of $$T_pM$$ and $$\tau(L)$$ the scalar curvature of of the subspace $$L$$ of $$T_pM$$, for each unordered k-tuple $$(n_1, \ldots, n_k)$$ of integers larger than or equal to two, satisfying $$d>n_1$$ and $$n_1 + \ldots + n_k < d$$ the δ-invariant $$\delta(n_1, \ldots, n_k)(p)$$ is defined as


 * $$\delta(n_1, \ldots, n_k)(p) = \tau(T_pM)-inf \lbrace \tau(L_1) + \ldots + \tau(L_k) \rbrace $$

with $$L_1, \ldots, L_k$$running over all $$k$$ mutually orthogonal subspaces of the tangent space of $$M$$ at $$p$$ such that $$dim L_j = n_j$$