| Summary: | The space <inline-formula> <math display="inline"> <semantics> <mo>Π</mo> </semantics> </math> </inline-formula> of centered <i>m</i>-planes is considered in projective space <inline-formula> <math display="inline"> <semantics> <msub> <mi>P</mi> <mi>n</mi> </msub> </semantics> </math> </inline-formula>. A principal bundle is associated with the space <inline-formula> <math display="inline"> <semantics> <mo>Π</mo> </semantics> </math> </inline-formula> and a group connection is given on the principal bundle. The connection is not uniquely induced at the normalization of the space <inline-formula> <math display="inline"> <semantics> <mo>Π</mo> </semantics> </math> </inline-formula>. Semi-normalized spaces <inline-formula> <math display="inline"> <semantics> <msup> <mo>Π</mo> <mn>1</mn> </msup> </semantics> </math> </inline-formula>, <inline-formula> <math display="inline"> <semantics> <msup> <mo>Π</mo> <mn>2</mn> </msup> </semantics> </math> </inline-formula> and normalized space <inline-formula> <math display="inline"> <semantics> <msup> <mo>Π</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msup> </semantics> </math> </inline-formula> are investigated. By virtue of the Cartan−Laptev method, the dynamics of changes of corresponding bundles, group connection objects, curvature and torsion of the connections are discovered at a transition from the space <inline-formula> <math display="inline"> <semantics> <mo>Π</mo> </semantics> </math> </inline-formula> to the normalized space <inline-formula> <math display="inline"> <semantics> <msup> <mo>Π</mo> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msup> </semantics> </math> </inline-formula>.
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