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This paper is devoted to the problem of corner detection in manifold-valued images and in vector fields on manifolds. Our solution is a generalization of the Harris corner detector. As in the grayscale case, our algorithm is based on an estimation of a self-similarity of a point neighborhood. We define the self-similarity for the general cases and obtain approximations of it by an action of a bilinear form. This form can be viewed as a generalization of the structure tensor. The generalized structure tensor is then used as usual in the corner detection procedure. Finally, we describe future experiments: the algorithm will be tested on a task of chemical compounds classification.