# Tagged Questions

For questions on manifolds of dimension $n$, a topological space that near each point resembles $n$-dimensional Euclidean space.

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### First and second fundamental form with rotational surfaces (check)

I'm working out some examples for surfaces in differential geometry. I was working out simple rotational surface, but I think I've done something wrong. Let $\gamma\left(t\right)$ a curve ...
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### Calabi-Yau $3$-fold given as elliptically fibered manifold over $\mathbb{C}P^1 \times \mathbb{C}P^1$

Consider a Calabi-Yau three-fold given as an elliptically fibered manifold over $\mathbb{C}P^1 \times \mathbb{C}P^1$$y^2 = x^3 + f(z_1, z_2)x + g(z_1, z_2),$$where$z_1$,$z_2$represent the two$\...
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### Uniqueness of connected sum

Connected sum is defined as Wiki .But I think the result of connected sum is not unique. For example ,make connected sum on $S^2$ with itself . Then , the result can be $T^2$ or Klein bottle. Is it ...
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### Introduction to morse theory with applications to optimization

I am wondering if there are any easy-to-read introduction materials on morse theory (especially with applications to nonconvex optimization) for people with non-math background.