Finding the maximum area of isosceles triangle

dg.differential geometry – Calculation of the denote curvature below a regular perturbation Answer

Hello pricey customer to our community We will proffer you an answer to this query dg.differential geometry – Calculation of the denote curvature below a regular perturbation ,and the respond will breathe typical by way of documented data sources, We welcome you and proffer you fresh questions and solutions, Many customer are questioning concerning the respond to this query.

dg.differential geometry – Calculation of the denote curvature below a regular perturbation

Let $X: M^n to N^{n+1}$ breathe a Riemannian immersion. Write $g, A, nu, H$ for the primary elementary figure, second elementary figure, Gauss map and denote curvature of $X$ respectively. Consider the regular pertubation $X_u: M to N$ outline by $X_u := X + unu$, the place $u$ is flush. For diminutive sufficient $u$, we’ve that $X_u$ is an immersion.

In the particular illustration the place the dimension of the hypersurface is $n=2$ and the ambient manifold is Euclidean $N = mathbb{R}^{n+1}$, Nicolaos Kapouleas provides a calculation of the quadratic and better organize phrases denote curvature of $X_u$ in ‘Complete Constant Mean Curvature Surfaces in Euclidean Three-Space’, Appendix C.

Is there a reference or calculation of the denote curvature of $X_u$ (or its linear/quadratic phrases) within the extra common circumstances of when the dimension $n$ isn’t equal to $2$ and/or when the ambient manifold $N$ isn’t Euclidean?

we’ll proffer you the answer to dg.differential geometry – Calculation of the denote curvature below a regular perturbation query through our community which brings all of the solutions from a number of dependable sources.

Add comment