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Mathematical discipline which studies some properties of smooth manifolds, which allow to generalize calculus to beyond $\mathbb{R}^n$. General relativity is written in this language.

2 votes
1 answer
58 views

Question regarding Kronecker delta [closed]

Given that, $\frac{\partial A^\mu}{\partial A^\nu} = \delta^\mu _\nu$. How to reach $\frac{\partial A_\mu}{\partial A_\nu} = \delta_\mu ^\nu$ ?
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1 vote
1 answer
214 views

Null surfaces in Lorentzian manifold

Null Hypersurface of Lorentzian Manifold: A hypersurface that admits a null-like normal vector field($N^a$) to it. i.e. $g_{ab}N^a N^b=0$ (metric signature$(-1,1,1,1,...)$) In Minkowski spacetime the …
Antonio's user avatar
  • 27
3 votes
1 answer
532 views

Confusion regarding Geodesics

Suppose we have a causal curve and we can cover the causal curve by convex normal neighborhoods. We also know that, in convex normal neighborhood there will exist a unique geodesic inside the neighbor …
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