Summary
We assume that the 4D space-time manifoldsis embedded in the flat five-dimensional spaceR 5. Then we show that the embedded effect appears as an effective mass. It is related to the extrinsic curvature rather than to the intrinsic one. When the 4D submanifold satisfies a condition, the effective mass becomes positive and we observe the mass of a particle there larger than one on flat space-time, apparently,i.e. dark matter. Thus, our scheme indicates another possibility for the dark-matter problem.
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Matsutani, S. Quantum field theory on space-time submanifold inR 5 extrinsic-curvature effect. Nuovo Cim B 109, 493–497 (1994). https://doi.org/10.1007/BF02728390
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DOI: https://doi.org/10.1007/BF02728390