Let M be the smooth 2-manifold , x = p($\theta$, ) = (cos($\theta$)sin( ), sin($\theta$)sin( ), cos( ),0 $\le$$\theta$ $\le$ 2$\pi$, and let be a parametrization for M. If M is oriented by the differential 2-form = zdx dy, determine whether the parametrization p is orientation preserving or orientation reversing for M.

Question

Let M be the smooth 2-manifold  , x = p($\theta$,  ) = (cos($\theta$)sin(  ), sin($\theta$)sin( ), cos( ),0 $\le$$\theta$ $\le$ 2$\pi$, and let  be a parametrization for M. If M is oriented by the differential 2-form   = zdx dy, determine whether the parametrization p is orientation preserving or orientation reversing for M.

Quizplus · Accepted Answer

The Answer of Let M be the smooth 2-manifold  , x = p($\theta$,  ) = (cos($\theta$)sin(  ), sin($\theta$)sin( ), cos( ),0 $\le$$\theta$ $\le$ 2$\pi$, and let  be a parametrization for M. If M is oriented by the differential 2-form   = zdx dy, determine whether the parametrization p is orientation preserving or orientation reversing for M.

Let M Be the Smooth 2-Manifold , X = θ\thetaθ

Let M Be the Smooth 2-Manifold , X = $\theta$