Question: we denote The product manifold N x M admits two projection maps, which TN:NxMN T: NX M M. Prove that the sum of the

we denote The product manifold N x M admits two projection maps,

we denote The product manifold N x M admits two projection maps, which TN:NxMN T: NX M M. Prove that the sum of the induced maps of tangent bundles TTNTTM: T(N M) TN TM is a diffeomorphism.

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