Changes

Discuss variation in portrayal of ''v'' in d''f''(''u'', ''v''):

Discuss variation in portrayal of ''v'' in d''f''(''u'', ''v''):

# as ordinary vector in second component of product space '''B'''^''n'' × '''B'''^''n'',

* <p>as ordinary vector in second component of product space '''B'''^''n''&nbsp;&times;&nbsp;'''B'''^''n'',</p>

# as tangent vector map : ('''B'''^''n''&nbsp;&rarr;&nbsp;'''B''')&nbsp;&rarr;&nbsp;'''B''', dual to '''B'''^''n'' ?

 

# as tangent vector map : ('''D'''^''n''&nbsp;&rarr;&nbsp;'''B''')&nbsp;&rarr;&nbsp;'''B''', dual to '''D'''^''n'' ?

* <p>as tangent vector map : ('''B'''^''n''&nbsp;&rarr;&nbsp;'''B''')&nbsp;&rarr;&nbsp;'''B''', dual to '''B'''^''n'' ?</p>

 

* <p>as tangent vector map : ('''D'''^''n''&nbsp;&rarr;&nbsp;'''B''')&nbsp;&rarr;&nbsp;'''B''', dual to '''D'''^''n'' ?</p>

Discuss differential as map : T(''U'') = ''U''T&nbsp;&rarr;&nbsp;'''B'''.

Discuss differential as map : T(''U'') = ''U''T&nbsp;&rarr;&nbsp;'''B'''.