A couple of problems here. The index appears to be part of a class but there is no class definition so there should be more code than what you are showing. and PHP unlike HTML does not have a closing > (greater then sign in it) so this
<?php>//no such tag
//and there is no such tag as the below
</?php>
should be
<?php
//and
?>
the $this is used within the class itself but since there is no class defined none of the functions will work. Also in your form you are using 'short tags' namely here
<?=$_POST['email']?>" />
//and immediately after ir
<?=$obj_validationSet->getErrorByFieldName('email')?>
it would be better to use
<?php echo $_POST['email'] ?>" /><?php echo$obj_validationSet->getErrorByFieldName('email')?>
It look like you are referencing a class that will validate the form elements as well a email validation, connect to the database.
OOPs now I see the call for the class right here.
require_once('_includes/classes/validation/ValidationSet.php');
so try just fixing the <?php> and </?php> and try it again make <?php> just <?php and end the script with just ?> not </?php>