= Spacelike submanifold
In <metric signature> $(-,+,\ldots,+)$, a <spacelike submanifold> of a <Lorentzian manifold> has an induced <metric tensor> defining a <positive-definite quadratic form>. With the overall reversed <metric signature>, its induced <metric tensor> instead has only negative <eigenvalues>. The definition applies to any dimension: enclosing charge-integration surfaces in four dimensions are two-dimensional examples, whereas a spacelike <Cauchy hypersurface> in four dimensions is three-dimensional.
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