Hi everybody,

my question is the following: Let $(M^n,g)$ be a Riemannian manifold and $e_1,\ldots,e_n$ be an orthonomal frame in a point. Assume, that we now the sectional curvatures of all planes, spanned by these vectors, i.e. we know the components $R_{ijij}$ of the curvature tensor.

Is it then possible to calculate all other components $R_{ijkl}$?

The problem is, that if I want, e.g. to calculate $R_{ijik}$ by the polarization identity, I need to know the sectional curvature spanned by $e_1,e_j+e_k$ which I assume to be unknown.

Is it then possible to calculate, or at least to estimate the sectional curvature from above by $R_{ijij}$, $R_{jkjk}$ and $R_{ikik}$?