A smooth l-form on real projective space with vanishing integral along all geodesics is said to have zero energy. Such a I-form is necessarily the exterior derivative of a smooth function. We formulate a general version of this theorem for tensor fields on real projective space and prove it using methods of complex analysis. A key ingredient is the cohomology of involutive structures.
|Number of pages||14|
|Publication status||Published - Oct 1997|
- integral geometry
- involutive structure
- Radon transform